Intro to Collision

Q.

In a head-on elastic collision of a very heavy body moving at $v$ with a light body at rest, the velocity of the heavy body after the collision is:

1. $v$

2. $2v$

3. zero

4. $\frac{v}{2}$

Q. In the figure shown a cart moves on a smooth horizontal surface due to an external constant force of magnitude $F$. The initial mass of the cart is $M_0$ and velocity is zero. Sand falls on to the cart with negligible velocity at constant rate $\mu \text{kg/s}$ and sticks to the cart. The velocity of the cart at time $t$ is:

1. $\frac{Ft}{M_0+\mu t}$
2. $\frac{Ft}{M_0}{e}^{\mu t}$
3. $\frac{Ft}{M_0}$
4. $\frac{Ft}{M_0+\mu t}{e}^{\mu t}$

Q. The momentum p (in kg m/s) of a particle is varying with time t ( in s) as p= 2+3t square. The force acting on the particle at t= 3 s will be??

Q.

A ball of mass m falls vertically to the ground from a height $h_1$ and rebound to a height $h_2$. The change in momentum of the ball on striking the ground is

1. 

2. 

3. 

4. 

Q. A 1.0 kg ball drops vertically onto a floor from a height of 25 cm. It rebounds to a height of 4 cm. The coefficient of restitution for the collision is-

1. 0.16
2. 0.32
3. 0.4
4. 0.56

Q. In an elastic collision in the absence of external forces, which of the following is correct?

1. The linear momentum is conserved
2. The linear momentum changes in collision
3. The final kinetic energy is more than the initial kinetic energy
4. The final kinetic energy is less than the initial kinetic energy

Q. Two point masses connected by an ideal string are placed on a smooth horizontal surfaces as shown in the diagram. A sharp impulse of $10\text{kg-m/s}$ is given to the $5\text{kg}$ mass. The velocity of the $10\text{kg}$ mass just after application of impulse will be $\frac{1}{x}\text{m/s}$, then value of $x$ is

Q. A particle of mass $3\text{kg}$ has been acted upon by a force $F\left(\text{N}\right)$ whose variation with time $\left(\text{s}\right)$ is shown in the figure.


If the particle is moving along a straight line with initial velocity of $4\text{m/s}$, then find the final velocity of the particle.

1. $5.33\text{m/s}$
2. $14.5\text{m/s}$
3. $2\text{m/s}$
4. $8.83\text{m/s}$

Q.

What is momentum ?Why do we study momentum

Q. Which of the following graphs can represent the relation between momentum (P) and kinetic energy (K) for a body in motion?

1. 
   
2. 
   
   
3. 
   
4. None of these

Q. What is the percentage increase in the linear momentum if the kinetic energy of the body is increased by 800 percent?

Q. Two balls of masses $2\text{kg}$ and $4\text{kg}$ are moving towards each other with speeds $6\text{m/s}$ and $4\text{m/s}$ respectively, on a frictionless surface. If the coefficient of restitution is $0.5$, the relative velocity of seperation between the two balls is

1. $1\text{m/s}$
2. $2\text{m/s}$
3. $5\text{m/s}$
4. $-1\text{m/s}$

Q. A particle of mass $1\text{kg}$ is initially at rest. A force starts acting on it in one direction whose magnitude changes with time. The (F - t) graph is shown in figure. The velocity of the particle at the end of $10\text{s}$ is

1. $150\text{m/s}$
2. $120\text{m/s}$
3. $100\text{m/s}$
4. $112.5\text{m/s}$

Q. Force-time$\left(\text{F - t}\right)$ graph of a rocket of mass 1000 kg shown below describes the force on the rocket. Neglecting gravity, the velocity of rocket $16\text{s}$ after starting from rest is

1. $100\text{m/s}$
2. $150\text{m/s}$
3. $200\text{m/s}$
4. $250\text{m/s}$

Q. A glass marble whose mass is 20 gm, falls from a height of 2.5 m and rebounds to a height of 1.6 m. Find the change in momentum due to its fall

Q. When two bodies are colliding:

1. Both should be in physical contact with each other at least once.
2. Both should be in physical contact with each other all the time.
3. Both may or may not be in physical contact.
4. Both should not be in physical contact with each other.

Q. A ball is projected from a top of height, h = 45 m. It is projected horizontally with an initial speed of 30 m/s. Then, which of the following statement is incorrect?

1. Ball will hit ground after 3 seconds
2. Ball will hit ground with speed $30\sqrt{2}m/s$
3. Ball will hit ground at angle ${45}^{\circ }$ with horizontal
4. Change in momentum of ball is in horizontal direction

Q. When two bodies are colliding:

1. Both should be in physical contact with each other all the time.
2. Both should be in physical contact with each other at least once.
3. Both may or may not be in physical contact.
4. Both should not be in physical contact with each other.

Q.

Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components p_x, p_y and p_z. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.

Q. Two objects that are moving in the $xy$ plane on a frictionless floor collide head on. Assume that they form a closed isolated system. The following table gives the momentum components in $\text{kg m/s}$ before and after the collision. What are the missing values $(a,b)$ (in $\text{kg m/s}$)?
$$\begin{array}{ccccc}& \text{Before collision along X-axis}& \text{Before collision along Y-axis}& \text{After collision along X-axis}& \text{After collision along Y-axis}\\ \text{Object}& P_{xi}& P_{yi}& P_{xf}& P_{yf}\\ A& -4& 5& 3& a\\ B& b& -2& 4& 2\end{array}$$

1. $11,1$
2. $10,11$
3. $5,7$
4. $1,11$

Q. Two balls of masses 2 kg and 1 kg have velocities 1 m/s and 2 m/s respectively. If you stop the 2 kg ball with right hand and 1 kg ball with the left hand. Which hand will hurt more?

1. Left Hand
2. Right Hand
3. Same for Both
4. Can’t be determined

Q.

Road accidents at high speeds are very much worse than accidents at low speeds. Why?

Q. If momentum of an object is increased by 10% then its K. E. Will increase by

Q. how much time is required for a force of 2 n to produce a change of 0.6kgm/s in the momentum of a body

Q. A $1800-kg$ car is stopped at a traffic light is struck from the rear by a $900-kg$ car. The two cars become entangled, moving along the same path as that of the originally moving car . If the smaller car was moving at $20m/s$ before the collision. What is the velocity of the entangled cars after the collision?

Q.

A particle circulating in a circular path has angular momentum L if its rotational kinetic energy is halved and frequency is doubled then what will be angular momentum

Q. When you hit a wall and a piece of sponge with equal force, then

1. Hitting a wall will hurt more
2. Hitting a piece of sponge will hurt more
3. Both will hurt equally
4. No comparison between two

Q. The physical quantity which is conserved for all types of collisions when no external force is acting on the system is:

1. Mass
2. Momentum
3. Kinetic energy
4. Length

Q. The force $F$ acting on a particle of mass $m$ is indicated by the force - time graph shown below. The change in momentum of the particle over the time interval from $0$ to $8\text{s}$ is

1. $12\text{N-s}$
2. $20\text{N-s}$
3. $18\text{N-s}$
4. $24\text{N-s}$

Q. Two objects that are moving in the $xy$ plane on a frictionless floor collide head on. Assume that they form a closed isolated system. The following table gives the momentum components in $\text{kg m/s}$ before and after the collision. What are the missing values $(a,b)$ (in $\text{kg m/s}$)?
$$\begin{array}{ccccc}& \text{Before collision}& & \text{After collision}& \\ \text{Object}& P_x& P_y& P_x& P_y\\ A& -4& 5& 3& a\\ B& b& -2& 4& 2\end{array}$$

1. $11,1$
2. $10,11$
3. $5,7$
4. $1,11$