Work Energy Theorem Application

Q.

Two spherical bodies of mass m and 5m, radius R and 2R respectively are released in free space with an initial separation of 12 R between their centres. If they attract each other due to gravitational force alone, then the distance covered by the smaller body just before the collision is

1. 2.5 R
2. 4.5 R
3. 7.5 R
4. 1.5 R

Q. A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table

1. 7.2 J
2. 3.6 J
3. 120 J
4. 1200 J

Q. If the error in measurement of momentum of a particle is 10% and mass is known exactly, the permissible error in the determination of kinetic energy is ___

Q. The mass of the bob of a simple pendulum of length $L$ is $m$ . If the bob is left from its horizontal position then the speed of the bob and the tension in the thread in the lowest position of the bob will be respectively.

1. $\sqrt{2gL}$ and $3mg$
2. $\sqrt{gL}$ and $3mg$
3. $\sqrt{2gL}$ and $4mg$
4. $\sqrt{gL}$ and $2mg$

Q. Three equal masses of $1\text{kg}$ each are placed at the vertices of an equilateral triangle $\text{PQR}$ and a mass of $2\text{kg}$ is placed at the centroid $O$ of the triangle which is at a distance of $\sqrt{2}\text{m}$ from each of the vertices of the triangle. The net force (in Newton), acting on the mass of $2\text{kg}$ is

1. $2$
2. $\sqrt{2}$
3. $1$
4. zero

Q. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = $\gamma t,$ where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

1. The force applied on the particle is constant
2. The speed of the particle is proportional to time
3. The distance of the particle from the origin increases linearly with time
4. The force is conservative

Q.

The P-V diagram for a cyclic process is a triangle ABC drawn in order. The co-ordinates of A, B and C are $(4,1),(2,4),$ and $(2,1)$ respectively. Calculate the work done in the complete cycle.

1. $3J$
2. $3\times {10}^{-3}J$
3. $6\times {10}^{-3}J$
4. $6J$

Q.

A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then

1. Lorry will come to rest in a shorter distance

2. None of the above

3. Car will come to rest in a shorter distance

4. Both come to rest in a same distance

Q. A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is

1. 
2. 
3. 
4. 

Q.

A bullet of mass 0.012 kg and horizontal speed $70m{s}^{-1}$ strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.

Q.

A stone of mass $1kg$is raised through $1m$a height

1. The loss of gravitational potential energy by the stone is $1joule$

2. The gain of gravitational potential energy by the stone is $1joule$

3. The loss of gravitational potential energy is $9.8joule$

4. The gain of gravitational potential energy is $9.8joule$

Q.

The same retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance will be

1. Doubled

2. The same

3. Halved

4. Four times

Q. A mass $m$ is revolving in a vertical circle at the end of a string of length $20\text{cms}$. By how much does the tension of the string at the lowest point exceed the tension at the topmost point

1. $6mg$
2. $2mg$
3. $mg$
4. $4mg$

Q. A string with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass $M=2\text{kg}$ attached to it at a distance of 1 m from the wall. A mass $m=0.5\text{kg}$ attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed in m/s upto 1 decimal place with which the mass $M$ will hit the wall when the mass m is released and $g=9.8{\text{ms}}^{-2}$?

Q.

What is a vertical circular motion? Show that the motion of an object revolving in a vertical circle is non-uniform in motion.

Q.

A light body and a heavy body have same linear momentum. Which one has greater K.E.?

Q.

The only force acting on a 2.0 kg body as it moves along the x - axis varies as shown in the figure. The velocity of the body at x = 0 is 4.0 $\frac{m}{s}$ What is the maximum K.E attained by the body between x=0 and x=5 m?

1. 18 J

2. 20 J

3. 16 J

4. 12 J

Q.

A uniform rod of length L lies on a smooth horizontal table. A particle moving on the table strikes the rod perpendicularly at an end and stops. Find the distance traveled by the centre of the rod by the time it turns through a right angle. Show that if the mass of the rod is four times that of the particle, the collision is elastic.

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 shell will be:

Q. Two identical wires A and B, each of length '$l$', carry the same current $I$. Wire A is bent into a circle of radius $R$ and wire B is bent to form a square of side '$a$'. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is

1. $\frac{{\pi }^2}{8}$
2. $\frac{{\pi }^2}{16\sqrt{2}}$
3. $\frac{{\pi }^2}{16}$
4. $\frac{{\pi }^2}{8\sqrt{2}}$

Q.

Figure (8-E7) shows a spring fixed at the bottom end of Ae:.. an incline of inclination. ${37}^{\circ }$ A small block of mass 2 kg starts slipping down the incline from a point 4.8 m away from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 in up the incline. Find (a) the friction : coefficient between the plane and the block and (b) the v spring constant of the spring. Take$g=10m/s^2$

Q.

Determine the velocity of a body of mass $100g$ having a kinetic energy of $20J$.

Q.

In figure (12-E3) $k=100N{m}^{-1},M=1kg$ and $F=10N.$ (a) Fine the compression of the spring in the equilibrium position. (b) A sharp blow by some external agent imparts a speed of $2m{s}^{-1}$ to the block towards left. Find the sum of the potential energy of the spring and the kinetic energy of the block at this instant. (c) Find the time period of the resulting simple harmonic motion. (d) Find the amplitude. (e) Write the potential energy of the spring when the block is at the left extreme. (f) Write the potential energy of the spring when the block is at the right extreme.

The answers of (b), (e) and (f) are different. Explain why this does not violate the principle of conservation of energy.

Q. A man applies a constant force of $5\text{N}$ on an object of mass $2\text{kg}$ and displaces it by $5\text{m}$. The object was initially at rest. The final velocity of object is

1. $10\text{m/s}$
2. $5\text{m/s}$
3. $25\text{m/s}$
4. $15\text{m/s}$

Q. The kinetic energy of a particle moving along a straight line increases uniformly with respect to the distance travelled by it. The force acting on the particle is ( $v$ is the speed of particle at any time)

1. Constant
2. inversely proportional to $v$
3. Proportional to $v$
4. Proportional to $v^2$

Q. A Carnot engine takes 3×10^6cal of heat from a Reservoir at 627°cand gives to async at 27 °c the work done by the engine is

Q.

Two springs A and B ($k_A$ = 2$k_B$) are stretched by applying forces of equal magnitudes at the four ends. If the energy stored in A is E, that in B is

1. 2E

2. 

3. E

4. 

Q.

The natural length of a spring is $60cm$ and its spring constant is $4000\frac{N}{m}$. A mass of $20kg$ is hung from it. The extension produced in the spring is (Take g = $9.8m/s^2$)

Q. A bullet of mass $50\text{g}$ leaves a rifle at an initial velocity of $2000\text{m/s}$ and strikes the earth at the same level with a velocity of $1000\text{m/s}$. The work done in overcoming the resistance of air will be

1. $750\text{J}$
2. $7.5\times {10}^3\text{J}$
3. $4500\text{J}$
4. $7.5\times {10}^4\text{J}$

Q.

An unloaded bus and a loaded bus are both moving with the same kinetic energy. The mass of the latter is twice that of the former. Brakes are applied to both, so as to exert equal retarding force. If $x_1$and $x_2$ be the distance covered by the two buses respectively before coming to a stop, then

1. 

2. 

3. 

4.