Work Done in Collision

Q. How to find the area under acceleration-displacement curve ?

Q.

A bullet of mass 20 g horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a level surface.The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest.Find the friction coefficient between the block and the surface.

Q. A bullet is fired at a plank of wood with a speed of 100 $m/s$. After passing through the plank, its speed reduces to 49 $m/s$. An another bullet of same mass and same size but moving with a speed of 200 $m/s$ is fired at the same plank. The speed of this bullet after passing through the plank will be approximately (Assume the resistance offered by the plank is same for both the bullets.)

1. 200 $m/s$
2. 149 $m/s$
3. 160 $m/s$
4. 180 $m/s$

Q.

Pascal is the unit of ____________.

Q. A force exerts an impulse $I$ on a particle changing its velocity from initial velocity $u\text{m/s}$ to final velocity $-2u\text{m/s}$. If the applied force and initial velocity are oppositely oriented along the same line, find the work done by force.

1. $\frac{1}{2}|I|u$
2. $\frac{3}{2}|I|u$
3. $\frac{1}{3}|I|u$
4. $2|I|u$

Q.

A man of weight $60kgwt$ takes a body of mass $15kg$ at a height $10m$ on a building in $3minutes$. The efficiency of man is

1. $10\%$

2. $20\%$

3. $30\%$

4. $40\%$

Q.

Derive the unit of energy in terms of the fundamental unit of SI system.

Q. A force exerts an impulse $I$ on a particle changing its velocity from initial velocity $u\text{m/s}$ to final velocity $-2u\text{m/s}$. If the applied force and initial velocity are oppositely oriented along the same line, find the work done by force.

1. $\frac{1}{2}|I|u$
2. $\frac{3}{2}|I|u$
3. $\frac{1}{3}|I|u$
4. $2|I|u$

Q. A wooden block of mass $M$ rests on a horizontal surface. A bullet of mass $m$ moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance $x$ on the surface. If the coefficient of friction between wood and the surface is $\mu$, the speed of the bullet at the time of striking the block is (where $m$ is mass of the bullet)

1. $\sqrt{\frac{2Mg}{\mu m}}$
2. $\sqrt{\frac{2\mu mg}{Mx}}$
3. $\sqrt{2\mu gx}\left(\frac{M+m}{m}\right)$
4. $\sqrt{\frac{2\mu mx}{M+m}}$

Q. A bullet of mass $20$g travelling horizontally with a speed of $500$m/s passes through a wooden block of mass $10.0$kg initially at rest on a surface. The bullet emerges with a speed of $100$m/s and the block slides $20$cm on the surface before coming to rest, the coefficient of friction between the block and the surface. $(g=10m/s^2)$.

1. $0.16$
2. $0.8$
3. $0.32$
4. $0.24$

Q.

Which one of the following pair of quantities has same dimension?

1. Force and work done

2. Momentum and impulse

3. Pressure and force

4. Surface tension and stress

Q. A woman pushes a trunk on a railway platform which has a rough surface. She applies a force of $100N$ over a distance of $10m$. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to $50N$. The total distance through which the trunk has been moved is $20m$. Plot the force applied by the woman and the frictional force, which is $50N$ versus displacement. Calculate the work done by the two forces over $20m$.

Q.

What is the work to be done to increase the velocity of a car from $30km{h}^{-1}$ to $60km{h}^{-1}$? If the mass of the car is $1500kg$?

Q. In a hydraulic lift, compressed air exerts a force $F_1$ on a small piston having a radius of $5\text{cm}$. This pressure is transmitted to a second piston of radius $15\text{cm}$. If the mass of the load to be lifted is $1350\text{kg}$, calculate the pressure acting on the smaller piston.
[Take $g=10{\text{m/s}}^2$]

1. $3\times {10}^5\text{Pa}$
2. $2\times {10}^5\text{Pa}$
3. $1.9\times {10}^5\text{Pa}$
4. $1.9\text{Pa}$

Q. A hydraulic automobile lift is designed to lift cars with a maximum mass of $300\text{kg}$. The area of cross-section of the piston carrying the load is $500{\text{cm}}^2$. What maximum pressure would smaller piston have to bear?

1. ${2.94\times 10}^4\text{Pa}$
2. ${11.66\times 10}^4\text{Pa}$
3. ${5.88\times 10}^4\text{Pa}$
4. ${8.55\times 10}^4\text{Pa}$

Q. An ideal spring is connected to the center of a solid cylinder. Initially the spring is compressed and compression is $40cm$. Now the cylinder is released from rest. Find the speed of the top point of the cylinder when the spring gains its relaxed length. (assuming friction between cylinder and ground is sufficient for pure rolling or rolling without slipping)

1. $10.4m/s$
2. $10.4m/s$
3. $22.4m/s$
4. $18.2m/s$

Q.

Define: Pressure.

Q. A bullet of mass $10g$ leaves a rifle at an initial velocity of $1000m/s$ and strikes the earth at the same level with a velocity of $500m/s$. the work done in joules overcoming the resistance of air will be

1. $3750$
   
2. $375$
   
3. $500$
   
4. $5000$
   

Q.

How much pressure is exerted by the foot of a chair having a weight of 100 N, which is equally distributed on each foot of the chair with an area of 25 $c{m}^2$?

Q. Under what condition can we write $F=ma$?

Q. Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will :

1. increase
2. decrease
3. remain same
4. decrease for some, while increase for others

Q. A body of mass $4kg$ is moving with momentum of $8kgm{s}^{-1}$. A force of $0.2N$ acts on it in the direction of motion of the body for $10s$. The increase in kinetic energy is:

1. $10J$
2. $4.5J$
3. $8.5J$
4. $4J$

Q. A wagon of $m$ can move without friction along horizontal rails. A simple pendulum consisting of a sphere of mass $m$ is suspended from the ceiling of the wagon by a string of length $l$. At the initial moment the wagon and the pendulum are at rest and the string is deflected through an angle ${60}^o$ from the vertical. Find the velocity of the wagon when the pendulum passes through the mean position.

1. $\sqrt{gl}$
2. $\sqrt{2gl}$
3. $\sqrt{\frac{gl}{2}}$
4. $2\sqrt{gl}$

Q. A block of density 2000 $kg/m^3$ and mass 10 kg is suspended by a spring stiffness 100 N/m. The other end of the spring is attached to a fixed support. The block is completely submerged in a liquid of density 1000 $kg/m^3$. If the block is in equilibrium position then,

1. the elongation of the spring is 1 cm.
2. the magnitude of buoyant force acting on the block is 50N.
3. the spring potential energy is 12.5 J.
4. magnitude of spring force on the block is greater than the weight of the block.

Q. The speed of an object of mass $2kg$ increases from $2m/s$ to $4m/s$ in $3s$. Find out the total work done on the object during this time interval?

1. $4J$
2. $6J$
3. $12J$
4. $24J$
5. $36J$

Q. The displacement x (in m), of a particle of mass m (in Kg) is related to time t (in sec) by $t=\sqrt{x}+3$. Find the work done in the first six seconds. (in mJ)

Q. Calculate the work done by the brakes of a gas of mass 1000 kg when its speed in reduced from 20 m/s or 10 m/s?

Q. A bullet of mass 50 g moving with velocity 200 m/s penetrates a wooden block of mass 5 kg suspended through a string from rigid support and comes to rest inside it. If length of the string is 10 m find the angular deflection of the string.

Q. Two children are playing a game in which they try to hit a small box on the floor with a marble fired from a spring-loaded gun that is mounted on a table. The target box is horizontal distance $D=2.20m$ from the edge of the table;see Fig.$8-48.$ Bobby compresses the spring $1.10cm,$ but the center of the marble falls $27.0cm$ short of the center of the box. How far should Rhoda compress the spring to score a direct hit? Assume that neither the spring nor the ball encounters friction in the gun.

Q. A bullet of mass $10\text{g}$ leaves a rife at an initial velocity of $3000\text{m/s}$ and strikes the earth at the same level with a velocity of $2000\text{m/s}$. The work done in overcoming the resistance of air will be

1. $2.5\times {10}^5\text{J}$
2. $2.5\times {10}^4\text{J}$
3. $2.5\times {10}^3\text{J}$
4. $2.5\times {10}^2\text{J}$