7Work, Energy, Power and Collision

📚
WORK, ENERGY, POWER AND COLLISION
▢ Work:
❖ Definition: Work is done when a body undergoes displacement under action of force
❖ Zero Work Examples:
  • •
    Man pushes object but displacement = 0
  • •
    Man rows boat upstream but remains at rest w.r.t. shore
  • •
    Centripetal force in circular motion
  • •
    Gravitational pull on satellite in circular orbit
  • •
    Person carrying load on head on horizontal road
  • •
    Car moving with uniform speed on frictionless road
❖ Formulae:

Table 1: Work Done

Case
Formula
Constant force
\(W=\vec F\cdot\vec s=Fs\cos\theta\)
Variable force
\(W=\int*{s_1}^{s_2}\vec F\cdot d\vec s=\int*{s_1}^{s_2}F\cos\theta\ ds\)
Work-energy theorem
\(W=\Delta K.E.\)
SI unit
Joule
CGS unit
Erg
Conversion
\(1\ Joule=10^7\ erg\)
❖ Sign of Work:

Table 1: Positive, Negative and Zero Work

Angle \(\theta\)
Work
Example
\(0\leq\theta<\frac{\pi}{2}\)
Positive
Force supports displacement
\(\frac{\pi}{2}<\theta\leq\pi\)
Negative
Friction; gravity during upward motion
\(\theta=\frac{\pi}{2}\)
Zero
Centripetal force
❖ Important Points:
  • •
    Work is scalar
  • •
    Work done does not depend on time taken
  • •
    Work done by a body → energy decreases
  • •
    Work done on a body → energy increases
▢ Power:
❖ Definition: Rate of doing work

Table 1: Power Formulae

Quantity
Formula / Unit
Power
\(P=\frac{Work}{Time}\)
Using force and displacement
\(P=\frac{\vec F\cdot\vec s}{t}\)
Instantaneous power
\(P=\vec F\cdot\vec v=Fv\cos\theta\)
Rate of energy change
\(P=\frac{\Delta E}{t}\)
SI unit
Watt
1 Watt
\(1\ W=1\ J\ s^{-1}\)
Practical unit
Horse power / HP
1 HP
\(746\ W\)
▢ Energy:
❖ Definition: Capacity of a body to do work
❖ Nature:
  • •
    Scalar quantity
  • •
    Same units and dimensions as work
  • •
    Mechanical energy = kinetic energy + potential energy
❖ Kinetic Energy:
◉ Definition: Energy possessed by body due to motion

Table 1: Kinetic Energy Formulae

Quantity
Formula / Point
Kinetic energy
\(E_k=\frac{1}{2}mv^2\)
In terms of momentum
\(E_k=\frac{p^2}{2m}\)
Momentum
\(p=\sqrt{2mE_k}\)
If \(E_k=0\)
\(p=0\)
Frame dependence
K.E. depends on frame of reference
◉ Frame Example: Person sitting in train: K.E. = 0 in train frame; K.E. = \(\frac{1}{2}mv^2\) in earth frame
◉ Stopping by Same Force:

Table 1: Stopping Distance and Time

Quantity
Formula
Stopping distance ratio
\(\frac{s_1}{s_2}=\frac{m_1v_1^2}{m_2v_2^2}\)
Stopping time ratio
\(\frac{t_1}{t_2}=\frac{m_1v_1}{m_2v_2}\)
◉ Bullet Through Planks:

Table 1: Bullet Special Cases

Condition
Result
Bullet loses \(\frac{1}{n}\) of velocity per plank
No. of planks = \(\frac{n}{2}+0.5\) if \(n\) odd; \(\frac{n}{2}+1\) if \(n\) even
Bullet loses \(\frac{1}{n}\) of velocity after penetrating distance \(x\)
Total distance before rest = \(\frac{n^2}{2n-1}x\)
Further distance after penetrating \(x\)
\(\frac{(n-1)^2}{2n-1}x\)
Bullet loses \(\frac{1}{n}\) of K.E. per plank
No. of planks = \(n\)
Bullet loses \(\frac{1}{n}\) of K.E. after distance \(x\)
Total distance = \(nx\)
Further distance after distance \(x\)
\((n-1)x\)
❖ Potential Energy:
◉ Definition: Energy stored due to configuration or position in a field
◉ Gravitational PE:

Table 1: Gravitational Potential Energy

Quantity
Formula
Potential energy at height \(h\)
\(U=-\frac{GMm}{R+h}=-\frac{mgR^2}{R+h}\)
Change in PE from surface to height \(h\)
\(\Delta U=\frac{mghR}{R+h}\)
If \(h\ll R\)
\(\Delta U=mgh\)
If \(h\gg R\)
\(\Delta U=mgR\)
◉ Special PE Formulae:

Table 1: Potential Energy Special Cases

Case
Increase in PE
Stick of length \(l\), pivoted at one end, displaced by \(\theta\)
\(\Delta U=\frac{mgl}{2}(1-\cos\theta)\)
Pendulum bob displaced by angle \(\theta\)
\(\Delta U=mgl(1-\cos\theta)\)
Elastic potential energy
\(U=\frac{1}{2}kx^2\)
◉ Sign of PE:
  • •
    Attractive forces → PE negative
  • •
    Repulsive forces → PE positive
❖ Work-Energy Theorem:
◉ Statement: Work done on a body equals change in kinetic energy
◉ Formula: \(W=\Delta K.E.=\frac{1}{2}mv_2^2-\frac{1}{2}mv_1^2\)
◉ Applications:

Table 1: Work-Energy Applications

Case
Work done / Result
Empty full tank to half depth
\(W=\frac{3}{8}Mgh\)
Take out all liquid from full tank
\(W=\frac{Mgh}{2}\)
Chain length \(l\), \(\frac{l}{n}\) hanging
\(W=\frac{mgl}{2n^2}\)
Released chain: velocity when end leaves edge
\(v=\frac{1}{n}\sqrt{(n^2-1)gl}\)
Rod of mass \(m\), length \(l\), made to stand on one end
\(W=\frac{mgl}{2}\)
❖ Conservative and Non-conservative Forces:

Table 1: Conservative vs Non-conservative Forces

Feature
Conservative force
Non-conservative force
Mechanical energy
Conserved
Not conserved
Work done
Depends only on initial and final positions
Depends on actual path
Closed path work
Zero
Not zero
Examples
Gravitational, electrostatic, magnetostatic, all central forces
Frictional, viscous forces
▢ Collision:
❖ Definition: Mutual interaction between particles for short time interval in which momentum and kinetic energy may change
❖ Law of Collision:
◉ Statement: Velocity of separation after collision is directly proportional to velocity of approach before collision

Table 1: Coefficient of Restitution

Quantity
Formula / Point
Velocity of separation
\(v_2-v_1\)
Velocity of approach
\(u_1-u_2\)
Relation
\(v_2-v_1=e(u_1-u_2)\)
Coefficient of restitution
\(e=\frac{v_2-v_1}{u_1-u_2}\)
Nature
Dimensionless and unitless
Elastic collision
\(e=1\)
Perfectly inelastic collision
\(e=0\)
Practical collision
\(0
◉ Notes:
  • •
    Linear momentum is conserved in every collision
  • •
    Total energy is conserved in every collision
  • •
    Kinetic energy is conserved only in elastic collision
❖ Types of Collision:

Table 1: Elastic vs Inelastic Collision

Feature
Elastic collision
Inelastic collision
Total energy
Conserved
Conserved
Linear momentum
Conserved
Conserved
Kinetic energy
Conserved
Not conserved
Coefficient of restitution
\(e=1\)
\(e<1\)
Perfectly inelastic collision
—
\(e=0\)
❖ Elastic Collision in One Dimension:
◉ Momentum Conservation: \(m_1u_1+m_2u_2=m_1v_1+m_2v_2\)
◉ Kinetic Energy Conservation: \(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\)
◉ Final Velocities:

Table 1: Elastic Collision Final Velocities

Quantity
Formula
\(v_1\)
\(v_1=\frac{(m_1-m_2)u_1+2m_2u_2}{m_1+m_2}\)
\(v_2\)
\(v_2=\frac{2m_1u_1+(m_2-m_1)u_2}{m_1+m_2}\)
◉ Special Cases:

Table 1: Elastic Collision Special Cases

Condition
Result
\(u_2=0\)
\(v_1=\frac{m_1-m_2}{m_1+m_2}u_1\), \(v_2=\frac{2m_1}{m_1+m_2}u_1\)
\(m_1=m_2\)
\(v_1=u_2\), \(v_2=u_1\); velocities exchange
\(m_1=m_2\), \(u_2=0\)
\(v_1=0\), \(v_2=u_1\)
\(m_1\ll m_2\), \(u_2=0\)
\(v_1\approx -u_1\), \(v_2\approx 0\)
\(m_1\gg m_2\), \(u_2=0\)
\(v_1\approx u_1\), \(v_2\approx 2u_1\)
❖ Inelastic Collision:
◉ Final Velocities with Coefficient e:

Table 1: Inelastic Collision Final Velocities

Quantity
Formula
\(v_1\)
\(v_1=\frac{m_1u_1+m_2u_2+em_2(u_2-u_1)}{m_1+m_2}\)
\(v_2\)
\(v_2=\frac{m_1u_1+m_2u_2+em_1(u_1-u_2)}{m_1+m_2}\)
◉ Perfectly Inelastic Collision:

Table 1: Perfectly Inelastic Collision

Quantity
Formula / Point
Bodies move with common velocity
\(v\)
Momentum equation
\(m_1u_1+m_2u_2=(m_1+m_2)v\)
Common velocity
\(v=\frac{m_1u_1+m_2u_2}{m_1+m_2}\)
Coefficient of restitution
\(e=0\)
Loss in K.E.
\(\frac{1}{2}\frac{m_1m_2}{m_1+m_2}(u_1-u_2)^2\)
❖ Body Dropped and Rebounds:
◉ Condition: Body dropped from height \(h_0\), strikes ground and rebounds to height \(h_1\)

Table 1: Rebound Formulae

Quantity
Formula
Striking velocity
\(u=\sqrt{2gh_0}\)
Velocity of bounce
\(v=eu=e\sqrt{2gh_0}\)
Coefficient of restitution
\(e=\frac{v}{u}=\sqrt{\frac{h_1}{h_0}}\)
Height after \(n\) bounces
\(h_n=e^{2n}h_0\)
Velocity after \(n\) bounces
\(v_n=e^n u\)
Momentum after \(n\) bounces
\(p_n=e^n p_0\)
Fractional loss in momentum after \(n\) bounces
\(\frac{\Delta p}{p_0}=1-e^n\)
K.E. after \(n\) bounces
\(K.E._n=e^{2n}K.E._0\)
Fractional loss in K.E. after \(n\) bounces
\(\frac{\Delta K.E.}{K.E._0}=1-e^{2n}\)
❖ Oblique Elastic Collision:
◉ Condition: Body of mass \(m_1\) collides elastically with body of mass \(m_2\), then both move at angles \(\alpha\), \(\beta\)

Table 1: Oblique Collision Equations

Conservation
Equation
Kinetic energy
\(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\)
Momentum along X-axis
\(m_1u_1+m_2u_2=m_1v_1\cos\alpha+m_2v_2\cos\beta\)
Momentum along Y-axis
\(m_1v_1\sin\alpha-m_2v_2\sin\beta=0\)
◉ Special Case: If \(m_1=m_2\) and \(u_2=0\), then \(\alpha+\beta=90^\circ\)
▢ Machines:

Table 1: Simple Machine Terms

Term
Formula
Mechanical advantage / MA
\(MA=\frac{Load}{Effort}=\frac{W}{P}\)
Velocity ratio / VR
\(VR=\frac{Distance\ travelled\ by\ effort}{Distance\ travelled\ by\ load}=\frac{D}{d}\)
Efficiency
\(\eta=\frac{MA}{VR}=\frac{W/P}{D/d}<1\)
Relation
\(MA
▢ Read and Digest:

Table 1: Important Points

Fact
Point / Formula
Flowing water
Has both K.E. and P.E.
Potential energy
Exists only for conservative forces
Energy change
Work is necessarily done
Static/dynamic equilibrium
Net work done = 0
Unstable equilibrium
Potential energy maximum
Air bubble rises in water
P.E. decreases because work is done by upthrust
Machine gun fires \(n\) bullets/s, each K.E. \(K\)
\(P=nK\)
Force to hold machine gun
\(F=np=n\sqrt{2mK}\)
Oscillation
Occurs about stable equilibrium only
Slope of work-time graph
\(P=\frac{dW}{dt}=\tan\theta\)
Gravity work
Positive downward, negative upward
Constant power motion
\(v\propto t^{1/2}\), \(s\propto t^{3/2}\), \(a\propto t^{-1/2}\)
Hydrogen balloon in air
Weight is negative; gravitational P.E. decreases with altitude
Like charges brought together
P.E. increases
Unlike charges brought together
P.E. decreases
Centripetal force
Power dissipated = 0
Water through pipe speed \(v\)
\(P=\frac{1}{2}\rho Av^3\)
Mass \(m\) from rest under constant force \(F\) for time \(t\)
Maximum power = \(\frac{F^2t}{m}\)
▢ High-Yield Recall:

Table 1: Work, Energy, Power and Collision One-Liners

Fact
Answer
Work
\(W=\vec F\cdot\vec s=Fs\cos\theta\)
Work nature
Scalar
SI unit of work
Joule
CGS unit of work
Erg
Joule-erg relation
\(1J=10^7\ erg\)
Work by centripetal force
Zero
Work by friction
Negative
Power
\(P=\frac{W}{t}=\vec F\cdot\vec v\)
1 HP
\(746\ W\)
Energy
Capacity to do work
Kinetic energy
\(\frac{1}{2}mv^2\)
K.E. in terms of momentum
\(\frac{p^2}{2m}\)
Momentum in terms of K.E.
\(p=\sqrt{2mE_k}\)
Elastic P.E.
\(\frac{1}{2}kx^2\)
Work-energy theorem
\(W=\Delta K.E.\)
Conservative force closed path work
Zero
Conservative forces
Gravitational, electrostatic, magnetostatic, central forces
Non-conservative forces
Frictional, viscous
Collision
Short-time mutual interaction
Coefficient of restitution
\(e=\frac{v_2-v_1}{u_1-u_2}\)
Elastic collision
\(e=1\)
Perfectly inelastic collision
\(e=0\)
Conserved in every collision
Linear momentum and total energy
K.E. conserved only in
Elastic collision
Equal masses elastic collision
Velocities exchange
Perfectly inelastic common velocity
\(v=\frac{m_1u_1+m_2u_2}{m_1+m_2}\)
Loss in K.E. in perfectly inelastic collision
\(\frac{1}{2}\frac{m_1m_2}{m_1+m_2}(u_1-u_2)^2\)
Rebound coefficient
\(e=\sqrt{\frac{h_1}{h_0}}\)
Height after n bounces
\(h_n=e^{2n}h_0\)
Velocity after n bounces
\(v_n=e^n u\)
Oblique elastic equal masses
Move perpendicular after collision
Mechanical advantage
\(MA=\frac{W}{P}\)
Velocity ratio
\(VR=\frac{D}{d}\)
Efficiency
\(\eta=\frac{MA}{VR}\)
Q1.
If a lift of mass 1000 kg moves upward with acceleration of 1 m/s then tension is:
📅BP 2011
Q2.
A boy started his journey from home to school which 16 km far at uniform speed 2.5 Km/hr and while returning, he returned with 4km/hr. What is his average speed?
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Q3.
Which is not graph of uniform motion:
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Q4.
A person on a moving train throws upwards a coin, and if it falls behind him, then train is
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Q5.
What is the total tension acting in figure?
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Q6.
A boat was crossing the river with velocity 40 m/s and river flowing with velocity 30 m/s. Then resultant velocity was:
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Q7.
If a lift of mass 500 Kg moves upward with acceleration 2 m/s then the tension is:
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Q8.
A body moves along with constant acceleration. Then its graphical representation will be:
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Q9.
A vehicle climbs a hill at speed of 40 km/hr and returns to same place at speed 60 km/hr. What is the average speed for whole journey?
Q10.
A man intends to cross a river on a boat with velocity 4 m/s. If resultant velocity of boat is 5 m/s. Then velocity of river is:
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Q11.
Which of the following speed time graph is not possible?
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Q12.
The slope of a velocity- time graph gives
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Q13.
Two bodies, one held I'm above the other directly, are released simultaneously and fall freely under gravity. After 3 second their relative separation will be
📅MOE 2013
Q14.
Time taken by a train of length 150 m and traveling with a uniform velocity of 6 km/hr to cross completely a bridge of length 1.5 km will be:
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Q15.
A body is thrown vertically upward and attains a velocity 15 m/s at half the maximum height. The maximum height upto the body can reach will be:
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Q16.
A body A is moving in north with 3 km/s and B with 4 km/s east. What is the relative velocity of a body A with respect to B.
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Q17.
A body moves 30m due north, 20m due east and 30sqrt(2) due south west. The total displacement covered by body from its initial position is:
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Q18.
Two bodies of mass '2 m' and 'm' are released from height '2H' and 'H' respectively. The ratio of time taken by\nthem to reach the ground is:
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Q19.
Two ships A and B are 4 km apart. A due west of B. If A moves with uniform velocity of 6 km/hr due south, calculate the magnitude of the velocity of A relative to B.
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Q20.
A body of mass 200 gm is thrown upwards with initial velocity of 30 m/s. What is total energy of body at height of 20 m from ground?
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Q21.
A body travels with velocity 30 m/s for 1st half of time and with velocity 40 m/s for 2nd half of time then what would be average velocity.
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Q22.
A body cover 1/3 rd distance with V1, velocity next 2/3 rd distance with V2 velocity the average velocity.
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Q23.
A person weighting 80 kg is standing on lift moves upward with a uniform acceleration of 4.9 m/s^2 then apparent wt. of the person is:
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Q24.
Two stones A and B are thrown from the top of a tower. The stone A is thrown vertically upward while the stone B is thrown vertically downward with the same speed. Which one of the following statements is true?
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Q25.
A meter rod pivoted at its one end is rotated through 120degree. Then displacement of its free end will be.
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Q26.
A person turns left or right by 90 after travelling each 20m in straight line. What is his maximum displacement after three successive turns?
Q27.
A person travels 3km towards north then 2km towards east and finally 2 sqrt(2) south-west. What is his displacement?
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Q28.
A flying kite travels 24m east then 8m south and finally 6m upward. What is its displacement from initial position?
Q29.
A racing car moving along circular track of radius R at constant speed v has described angle \\theta about centre of the track n certain time. What is the average velocity for the interval of time?
Q30.
A car travelling along circular track at constant speed 20m/s has completed half revolution on the track. Its average velocity will be [IOM/MOE/KU]
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Q31.
The length of a second hand in a watch is 1cm. The change in velocity in 15sec is
Q32.
If the displacement of a body is proportional to square of time. Then body has
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Q33.
The displacement of a particle moving in a straight line at any instant time t is given as x = t^2 + 20 (in metre). What is its average velocity for first four seconds?
Q34.
In the above question, what is its velocity at 4 second?
Q35.
The acceleration of a particle at any instant of time 't' which starts from origin at initial velocity 2m/s is a = 2t (in m/s^2). What is its velocity in 5 seconds?
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Q36.
A train of 150 meter length is going towards north direction at a speed of 1 m/sec. A parrot flies at the speed of 5m/sec towards south direction parallel to the railway track. The time taken by the parrot to cross the train is
Q37.
Two boys start running towards each other from two points, they are 120m apart. One runs with a speed of 5m/s and other with a speed of 7m/s. When and where do they meet each other from 1st point?
Q38.
A train of length 200m travelling at 30m/sec overtakes another train of length 300m travelling at 20m/sec. The time taken by first train to pass the second is
Q39.
An insect crawls a distance of 4m along north in 10seconds and then a distance of 3m along east in 5 seconds. The average velocity of the insect is:
Q40.
A vehicle moving along a straight road covers half distance of its journey a 40km/hr and next half distance at 60km/hr in same direction. The average velocity for entire journey is
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Q41.
A vehicle moving along a straight road travels for half time at 40 km/hr and then travels for next half time at 60 km/hr. The average velocity for entire journey is
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Q42.
A body moving in a straight line travels 2m/s for first half distance and second half distance is covered in two equal time intervals at 4m/s and 2m/s. What is its average velocity for entire journey?
Q43.
A body moving in a straight line travels 2m/s for first half time and for second half time it covers equal distance at velocities 4m/s and 2m/s. What is its average velocity for entire journey?
Q44.
A person travels certain distance x due east at constant velocity v, and then he travels equal distance x due north at constant velocity v2. What is his average velocity for entire journey?
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Q45.
A person travels for certain time t due east at constant velocity v, and then he travels for equal time t due north at constant velocity v2. What is his average velocity for entire journey?
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Q46.
The displacement of a particle is given by x = 2 -5t + 6t^2 where x is in meters and t in seconds. The initial velocity of the particle
Q47.
If x denotes displacement in time t, and x = a cost, the acceleration is
Q48.
A car travelling due east at 20m/s turns towards north without changing speed in 10sec. The average acceleration of the car for its turn is
Q49.
In the above question if the car makes 'U' turn then average acceleration of the car will be
Q50.
A car travelling due north at 30km/hr turns west and travels at the same speed, the change in velocity of car is
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Q51.
A body starts from rest and moves at constant acceleration a in a straight line for time t1, covering a distance x1, and then it retards at rest at constant deceleration b for time t2 covering a distance X2. Then average velocity will be
Q52.
A stone is dropped from the top of a tower. If it reaches the earth in 6 seconds, the height of the tower is nearly.
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Q53.
A car accelerates from rest at constant rate for the first 10seonds and covers a distance x. It covers a distance y in the next 10 seconds at the same acceleration. Which of the velocity is true?
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Q54.
A car accelerates at a constant rate a1 for time t1 and then retards at the constant\nrate a2 for time t2 and comes to rest t1/t2 =
Q55.
A person is throwing balls into the air one after the other. He throws the second ball when first ball is at the highest point. If he is throwing two balls every second, how high do they rise?
Q56.
A ball is dropped from the top of a tower 100m high. Simultaneously, another ball is thrown upwards with a speed of 50m/s. After what time do they cross each other?
Q57.
The engine of a motorcycle can produce a maximum acceleration 5m/s. Its brakes can produce a maximum retardation 10 m/s^2. What is the minimum time in which it can cover a distance of 1.5 km?
Q58.
Two balls A and B are simultaneously projected from the top of a building at 10m/s upwards and 20m/s downwards respectively. Find out the separation between them 3sec after projection.
Q59.
59.A stone is dropped from a certain height which can reach the ground is 5 second. It is stopped after three second of its fall and then is again released. The total time taken by the stone to reach the ground will be
Q60.
A balloon is going upwards with velocity 12m/s. It releases a packet when it is a height of 65m from ground. How much time will the packet take to reach the ground
Q61.
A car moving with a speed of 40km/hr can be stopped by applying brakes after at least 2m. If the same car is moving with speed of 80 km/hr, the minimum stopping distance is
Q62.
A ball is dropped from the top of a very high tower. Distance covered by it in last second of its motion equal to the distance covered by in first 3secs of its motion. Find the time of fall
Q63.
A ball thrown vertically upward covers equal distances in its fourth and fifth second. Then initial velocity of projection will be
Q64.
A ball is projected vertically upwards from the ground. It is found at the same elevation at t = 3s and t = 7s after projection. Find the projection speed.
Q65.
A stone is dropped from the top of a tower. If it covers 24.5m in the last second of its motion, the height of the tower is
Q66.
A body is projected vertically upward from point A, the top of a tower. It reaches the ground in t1 secs. If it is projected vertically downwards from A with the same velocity, it reaches the ground in t2 secs. If it falls freely from A, it would reach the ground in
Q67.
A body is released from top of a smooth inclined plane having inclination 30degree and takes 3secs to reach the bottom. If the angle of inclination is doubled keeping the height same, what will be the time taken for the same process?
Q68.
A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top?
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Q69.
A ball is dropped from the top of a building and its time of fall is 't'. In the last 1/4^th time of its fall, it travels 1.4 metres. Find out the height of the building
Q70.
A ball is projected vertically upwards from ground and its time of rise is 't'. In first t/5 time, it covers a distance of 2.7m. Find the height
Q71.
A body is thrown upwards with velocity 100m/s and it travels 5m in the last second of its upward journey. If the same body is thrown upwards with velocity 200m/s, what distance will it travel in the last second of upward journey?
Q72.
A body falls freely from rest and has velocity v after it falls through a height h. The distance it has to fall down further for its velocity to become double is
Q73.
A ball dropped downwards. After 1 second another ball is dropped downwards from the same point. What is the distance between them 3seconds after the first ball was dropped?
Q74.
Two bodies are thrown vertically upward with their initial velocities in ratio 2: 3. Then the ratio of maximum heights attained by them is
Q75.
A lion chases a deer 30m ahead of it and gains 3m in as alter the chase started. After 10s, the distance between them is
Q76.
A ball A is thrown vertically upward at initial speed u while another B is dropped from a height at the same instant. After time t, their relative velocity w.r.t one another will be
Q77.
A stone dropped from a height covers 5/9 part of total distance in last second. Then initial height will be
Q78.
Water drops are falling at regular intervals of time from a roof 5m high. When first drop strikes the ground, third drop just leaves the roof then height of the second drop from the ground at this\ninstant is
Q79.
A body thrown vertically upwards attains a maximum height H. While moving upwards if it covers first (3H/4) distance from the ground in time T, then time taken to cover remaining distance H/4 will be
📅IOM•MOE•KU•BPKIHS
Q80.
When a ball is thrown upwards with air resistance not neglected, it takes 10seconds to reach a height. It then returns to ground in time.
📅MOE
Q81.
A bullet loses 1/20 of its velocity after penetrating a plank. How may planks are required to stop the bullet?
Q82.
Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side l at t = 0. Each of the particle moves with constant speed v. A always has its velocity along AB, B along BC and C along CA. At what time will these particles meet each other?
Q83.
A vehicle moving at constant acceleration along a straight road has velocities u and v at two point A and B on the road. Then it velocity at midway between A and B will be
Q84.
A person who can swim at 5km/hr in still water, crosses a river 1 km wide flowing at 3km/hr along shortest route. Then time taken to cross the river is
Q85.
A person who can swim at 12km/hr in still water wants to cross a river flowing at 6km/hr along shortest route. Then he has to start swimming at
Q86.
A person who can swim at 5km/hr in still water cross a river 1km wide flowing at 3km/hr in shortest time. How far he will reach at another bank?
Q87.
To a person running due east at 8km/hr raindrops appear to fall vertically downward at 6km/hr. Then actual velocity of raindrops is
Q88.
A boat takes 2 hours to travel 8km and back in still water lake. If the velocity of water is 4km/hr, the time taken for going upstream of 8km and coming back is
Q89.
A stone is dropped from the top of a tower of height 'h'. It reaches the ground in 't' secs. The position of the stone after t/3 secs. will be ... from the ground
📅IOM 063
Q90.
A stone is dropped from the top of tower of height h. After 1 second another stone is dropped from balcony 20 m below the top. Both reach the bottom simultaneously. What is the value of h?
📅IOM 05
Q91.
A body of mass 'm' is released from height 'h' in time 't'. Then, acceleration is determined by:
📅IOM 2015
Q92.
When an aeroplane is moving with velocity 600km/h due east & return with 400km/hr,\nthen what is average speed if they travel same distance?
📅KU 2016
Q93.
A person is traveling at 4 m/s towards east. The rain is apparently falling vertically downwards with 3 m/s, then the actual velocity of rain is,
📅IOM 2016
Q94.
A train travels for 40 km with velocity of 80 km/hr and again it travels next 40 km with velocity of 40 km/hr. Then average speed of the train is
📅IOM 2016