Tag: collision of two rigid bodies

Questions Related to collision of two rigid bodies

A uniform rod AB of length $L$ and mass $M$ is lying on a smooth table. A small particle of mass $m$ strike the rod with a velocity $v _0$ at point C a distance x from the centre O. The particle comes to rest after collision. The value of $x$, so that point A of the rod remains stationary just after the collision,  is:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $L/3$

  2. $L/6$

  3. $L/4$

  4. $L/12$

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Correct Option: B

a body of mass m falls from height h on ground. If e be the coefficient of restitution of collision betwwen the body and ground then the distance travelled by body before it comes to rest is

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $h\left{ {\dfrac{{1\, + {e^2}}}{{1 - {e^2}}}} \right}$

  2. $h\left{ {\dfrac{{1\, - {e^2}}}{{1 + {e^2}}}} \right}$

  3. ${\dfrac{{2eh}}{{1 + {e^2}}}}$

  4. ${\dfrac{{2eh}}{{1 - {e^2}}}}$

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Correct Option: C

A solid spherical ball of radius R collides with a rough horizontal surface as shown in figure. At the time of collision its velocity is $v _{0}$ at an angle $\theta$ to the horizontal and angular velocity $\omega _{0}$ as shown. After collision, angular velocity of ball may

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. decrease

  2. increase

  3. remains constant

  4. none of these

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Correct Option: A

A particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When it moves from one point to a diametrically opposite point, its:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. momentum does not change

  2. momentum changes by $2Mv$

  3. $KE$ changes by $Mv^{2}$

  4. none of the above

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Correct Option: B

If a ball is dropped from rest, it bounces from the floor. The coefficient of restitution is $0.5$ and the speed just before the first bounce is $5\ m/sec$. The total time taken by the ball to come to rest is:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $2\ sec$

  2. $1\ sec$

  3. $0.5\ sec$

  4. $0.25\ sec$

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Correct Option: C

A solid sphere rolls without slipping on a rough horizontal floor, moving with a speed $v$. It makes an elastic collision with a smooth vertical wall. After impact,

physics systems of particles and rotational motion collision of two rigid bodies energy and collisions understanding collisions

  1. it will move with a speed $v$ initially.

  2. its motion will be rolling without slipping.

  3. its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant.

  4. its motion will be rolling without slipping only after some time.

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Correct Option: C,D
Explanation:

The velocity would abruptly change and would cause the solid sphere to slide at first and after some time it would attain a constant angular velocity where it would roll without slipping.

An athelete diving off a high spring board can perform a variety of physical moments in the air before entering the water below. Which one of the following parameters will remain constant during the fall? The athelete's:

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. linear velocity

  2. linear momentum

  3. moment of inertia

  4. angular velocity

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Correct Option: D

In an elastic collision, kinetic energy of the relative motion is converted into the ____ energies of two momentarily compressed bodies, and then is converted back into the _____ energy. Fill in the blanks. 

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. kinetic,kinetic

  2. elastic,kinetic

  3. elastic,elastic

  4. kinetic,elastic

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Correct Option: B
Explanation:

During elastic collision, at first both the bodies get deformed, so total kinetic energy is converted into theie elastic energies and then they regain their original shape (when moving apart with different velocities) suggesting that the elastic energy is converted back into the kinetic energy.

State whether the given statement is True or False :

In an elastic collision, the net kinetic energy of the two colliding bodies is conserved.

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. True

  2. False

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Correct Option: A
Explanation:

In an elastic collision, the net kinetic energy as well as linear momentum of the two colliding bodies is conserved. The given statement is true.

A ball of mass m moving with a constant velocity u strikes against a ball of same mass at rest. If e is the coefficient of restitution, then what will be the ratio of velocity of two balls after collision?

physics work, energy and power collision of two rigid bodies energy and collisions understanding collisions

  1. $\dfrac{1-e}{1+e}$

  2. $\dfrac{e-1}{e+1}$

  3. $\dfrac{1+e}{1-e}$

  4. $\dfrac{e+1}{e-1}$

Show answer
Correct Option: A
Explanation:

A. $\dfrac{1-e}{1+e}$


Given,


$m _1=m _2=m$ (say)

$u _1=u $, $u _2=0$

let, $v _1=$ velocity of ball 1 after collision

      $v _2=$ velocity of ball 2 after collision

The coefficient of restitution,

$e=\dfrac{v _2-v _1}{u _1-u _2}$

$eu=v _2-v _1$. . . . . . .(1)

By the conservation of Linear momentum,

$m _1u _1+m _2u _2=m _1v _1+m _2v _2$ 

$u=v _1+v _2$. . . . . . . . .(1)

By solving equation (1) and (2), we get

$v _1=\dfrac{(1-e)u}{2}$

$v _2=\dfrac{(1+e)u}{2}$

The ratio of velocity of two ball,

$\dfrac{v _1}{v _2}=\dfrac{1-e}{1+e}$