Impulse in Collsion Caveat's

Q. A large block of wood of mass $M$ $=5.99\text{kg}$ is hanging from two long massless cords. A bullet of mass $m=10\text{g}$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $h=9.8\text{cm}$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (take $g=9.8{\text{ms}}^{-2}$)

1. $831.4\text{m/s}$
2. $841.4\text{m/s}$
3. $811.4\text{m/s}$
4. $821.4\text{m/s}$

Q. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown. Initially the system is at rest when a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v$, the speed with which the system moves just after collision is

1. $\frac{v}{5}$
2. $\frac{v}{2}$
3. $\frac{v}{3}$
4. $\frac{v}{4}$

Q. A ball of mass 0.45 kg is heading towards a wall with a speed of 25 m/sec. After hitting the wall the ball bounces back with a speed of 20 m/sec. The ball was in contact with the wall for 0.003 seconds. What is the average force the wall exerts on the ball?

1. 760 N
2. 3000 N
3. 3750 N
4. 6750 N

Q. A body of mass $4kg$ is acted on by a force which varies as shown in figure. The momentum acquired is:

1. $280N-s$
2. $140N-s$
3. $70N-s$
4. $210N-s$

Q. A shell of mass $m$ moving with velocity $v$ suddenly breaks into 2 pieces. The part having mass $\frac{m}{4}$ remains stationary. The velocity of the other part will be:

1. $v$
2. $2v$
3. $\frac{3}{4}v$
4. $\frac{4}{3}v$

Q. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown. Initially the system is at rest when a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v$, the speed with which the system moves just after collision is

1. $\frac{v}{3}$
2. $\frac{v}{4}$
3. $\frac{v}{5}$
4. $\frac{v}{2}$

Q. A block of mass $m=1\text{kg}$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown in the figure. Initially the system is at rest when a particle of mass $1\text{kg}$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v=3\text{m/s}$. Find the speed with which the system moves just after collision

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

Q. A system of two blocks A and B are connected by an inextensible massless string as shown in figure. The pulley is massless and frictionless. Initially, the system is at rest. A bullet of mass 'm' moving with a velocity 'u' as shown hits block 'B' and gets embedded into it. The impulse imparted by tension force to the block of mass 3m is :

1. $\frac{5mu}{4}$
2. $\frac{4mu}{5}$
3. $\frac{2mu}{5}$
4. $\frac{3mu}{5}$

Q. What is the meaning of static procedure of measuring force?

Q. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown. Initially the system is at rest when a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v$, the speed with which the system moves just after collision is

1. $\frac{v}{3}$
2. $\frac{v}{4}$
3. $\frac{v}{5}$
4. $\frac{v}{2}$

Q. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown. Initially the system is at rest when a particle of mass $m$ falls on the pan and sticks to it. If the particle strikes the pan with a speed $v$, the speed with which the system moves just after collision is

1. $\frac{v}{3}$
2. $\frac{v}{4}$
3. $\frac{v}{5}$
4. $\frac{v}{2}$