Momentum

Q. The point from where a ball of mass $2\text{kg}$ is projected is taken as the origin of the co-ordinate axes. The $x$ and $y$ components of its displacement are given by $x=6t$ and $y=8t-5t^2$. Find the change in its momentum ( in 𝒌𝒈 𝒎/𝒔) from $t=0$ to $t=2$ seconds.

1. $40$
2. $60$
3. $80$
4. $20$

Q. A projectile of mass $4M$ is fired at a speed of $100\text{m/s}$ at an angle of ${37}^{\circ }$ from the horizontal. At the highest point, the projectile breaks into two parts with mass $M$ and $3M$. Mass $M$ falls down immediately after the explosion and mass $3M$ lands at some horizontal distance from mass $M$. Choose the correct statement. (Take $g=10{\text{m/s}}^2$)

1. None of the above
2. Time taken by $4M$ to reach the highest point and time taken by $3M$ to land on the ground from the highest point will be the same.
3. Time taken by $4M$ to reach the highest point and time taken by $3M$ to land on the ground from the highest point will be different.
4. Distance covered by $4M$ along the horizontal ground and distance covered by $3M$ along the horizontal ground will be the same.

Q. Figure shows the variation of force acting on a body with time. Assuming the body to start from rest the variation of its momentum with time is best represented by which plot?

1. 
2. 
3. 
4. 

Q. 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

1. Kinetic energy changes by $\frac{M{V}^2}{4}$
2. momentum does not change.
3. Momentum changes by $2MV$.
4. Kinetic energy changes by $M{V}^2$

Q. Six bullets of mass $5\text{gm}$ are fired from a gun of mass $5\text{kg}$. What is the speed of the gun if the speed of the bullets w.r.t. the ground is $200\text{m/s}$?

1. $1.2\text{m/s}$
2. $0.2\text{m/s}$
3. $200\text{m/s}$
4. $\frac{200}{6}\text{m/s}$

Q. A lead ball strikes a wall and falls down while a tennis ball having the same mass and velocity strikes the wall and bounces back. Check the correct statement.

1. The momentum of the lead ball is greater than that of the tennis ball.
2. The lead ball suffers a greater change in momentum compared with the tennis ball.
3. The tennis ball suffers a greater change in momentum as compared with the lead ball.
4. Both suffer an equal change in momentum.

Q. A nucleus of mass number '$A$' originally at rest emits an $\alpha$ particle with a speed '$v$' the recoil speed of the daughter nucleus is

1. $\frac{4v}{A+4}$
2. $\frac{2v}{4-A}$
3. $\frac{v}{A+4}$
4. $\frac{4v}{A-4}$

Q. A $1$ $kg$ stationary bomb is exploded in three parts having mass ratio $1:1:3$. Parts having same mass move in perpendicular directions with velocity $30$ $m/s$, then the velocity of bigger part will be:

1. $10\sqrt{2}$ $m/s$
2. $\frac{10}{\sqrt{2}}$ $m/s$
3. $15\sqrt{2}$ $m/s$
4. $\frac{15}{\sqrt{2}}$ $m/s$

Q. A metal cannonball of mass $m$ rests next to a tree at the very edge of a cliff $36.0m$ above the surface of the ocean. In an effort to knock the cannonball off the cliff, some children tie one end of a rope around a stone of mass $80.0kg$ and the other end to a tree limb just above the cannonball. They tighten the rope so that the stone just clears the ground and hangs next to the cannonball. The children release the stone, which then swings down and makes a head-on, elastic collision with the cannonball, projecting it horizontally off the cliff. The cannonball lands in the ocean a horizontal distance $R$ away from its initial position.
Find the horizontal component $R$ of the cannonball's displacement as it depends on $m$.

Q. A gun (mass = $M$) fires a bullet (mass = $m$) with speed $v_r,$ relative to barrel of the gun which is inclined at an angle of ${60}^o$ with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun.

1. $v=\frac{M{v}_r}{2(M+m)}$
2. $v=\frac{m{v}_r}{(M+m)}$
3. $v=\frac{m{v}_r}{\sqrt{2}(M+m)}$
4. $v=\frac{m{v}_r}{2(M+m)}$