Intro to Collision

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. $mg(h_1-h_2)$

2. $m(\sqrt{2g{h}_1}+\sqrt{2g{h}_2})$

3. $m\sqrt{2g(h_1+h_2)}$

4. $m\sqrt{2g}(h_1+h_2)$

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

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

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. 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. 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. 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. 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. A ball is moving with a velocity of $8\text{m/s}$ towards a surface which is also moving in a downward direction with velocity of $2\text{m/s}$ as shown in figure. After collision with the surface, ball rebounds back. If the coefficient of restitution is $e=0.5$, find the rebound velocity of the ball. (Given:Velocity of surface will be same even after collision and all other external forces are absent.)

1. $5\text{m/s}$
2. $1\text{m/s}$
3. $1.5\text{m/s}$
4. $0.5\text{m/s}$

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

1. $24\text{N s}$
2. $12\text{N s}$
3. $20\text{N s}$
4. $6\text{N s}$