Defining Kinetic Energy

Q. A particle performs uniform circular motion with an angular momentum $L$. If the frequency of particle's motion is doubled and its kinetic energy halved, the angular momentum becomes

1. $2\text{L}$
2. $4\text{L}$
3. $\frac{L}{2}$
4. $\frac{L}{4}$

Q. A disc rolls down a plane of length $L$ and inclined at angle $\theta$, without slipping. Its velocity on reaching the bottom will be

1. $\sqrt{\frac{2gL\sin \theta }{3}}$
2. $\sqrt{\frac{4gL\sin \theta }{3}}$
3. $\sqrt{4gL\sin \theta }$
4. $\sqrt{\frac{10gL\sin \theta }{3}}$

Q.

If the kinetic energy of a body becomes 4 times then what will be the percentage increase in its momentum. Please describe the calculation.

Q. The linear momentum of body is decreased by $20\%$. Then what is the $\%$ change in kinetic energy of the body.

1. $20\%$ decreased
2. $36\%$ decreased
3. $40\%$ decreased
4. $30\%$ decreased

Q. A ball is thrown vertically upwards with a velocity of $10\text{m/s}$. It returns to the ground with velocity of $9\text{m/s}$. If $g=9.8{\text{m/s}}^2$, then the maximum height attained by the ball is nearly (assume air resistance to be uniform)

1. $5.1\text{m}$
2. $4.1\text{m}$
3. $4.61\text{m}$
4. $5.0\text{m}$

Q. A cubical block A of mass 10 kg and a block B of mass 2 kg are connected via string-pulley system as shown in the figure. If one end of the string is pulled with a force 20 N as shown, then the acceleration of wedge will be (All surfaces are smooth. Pulley and strings are ideal)

Q. A particle moves on a rough horizontal ground with some initial velocity $v_0$. If ${\left(\frac{3}{4}\right)}^{th}$ of its kinetic energy is lost due to friction between the particle and the ground in time interval $t_0$, then find the coefficient of kinetic friction between the particle and ground. (Assume only kinetic friction is acting on the particle)

1. $\frac{v_0}{4g{t}_0}$
2. $\frac{v_0}{2g{t}_0}$
3. $\frac{3v_0}{4g{t}_0}$
4. $\frac{v_0}{g{t}_0}$

Q.

If kinetic energy of a body is increased by 300%, then percentage change in momentum will be

1. 100%
2. 150%
3. 265%
4. 73.2%

Q. A rifle bullets loses ${\left(\frac{1}{20}\right)}^{th}$ of its velocity in passing through a plank. Assuming that the plank exerts a constant retarding force, the least number of such planks required just to stop the bullet is

1. $11$
2. $21$
3. Infinite
4. $20$

Q.

The kinetic energy of a body is increased by $21\%$. What is the percentage increase in the magnitude of linear momentum of the body?

1. $100\%$
2. $11\%$
3. $21\%$
4. $10\%$

Q. A ball weighing 10 gram hits a hard surface vertically with a speed of 5 metre per second and rebounds with the same speed the ball remain in contact with the surface for 0.01 second the average force exerted by the surface on the ball is

Q. A particle suspended by a light inextensible thread of length $l$ is projected horizontally from its lowest position with a velocity $\sqrt{7gl/2}$. The string will slack after swinging through an angle $\theta$ with the horizontal. Then, $\theta$ is

1. ${30}^{\circ }$
   
2. ${90}^{\circ }$
   
3. ${45}^{\circ }$
   
4. ${37}^{\circ }$
   

Q.

A 300 g mass has a velocity of $(3\hat{i}+4\hat{j})m/s$ at a certain instant. What is its kinetic energy?

1. 1.35 J

2. 2.4 J

3. 3.75 J

4. 7.35 J

Q. A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x\text{m}$ into the sand, the average resistance offered by the sand to the body is

1. $Mg\left(\frac{h}{x}\right)$
2. $Mg(1+\frac{h}{x})$
3. $Mgh+Mgx$
4. $Mg(1-\frac{h}{x})$

Q. A homogeneous cylinder of mass M and radius R is pulled on a horizontal plane by a horizontal force For acting through its mass centre assuming rolling without slipping what is angular acceleration of cylinder

Q. A particle of mass $2\text{kg}$ starts moving in a straight line with an initial velocity of $2\text{m/s}$, at a constant acceleration of $2{\text{m/s}}^2$. Then, rate of change of kinetic energy

1. is four times the rate of change of velocity at any moment.
2. is constant throughout.
3. is four times the velocity at any moment.
4. is two times the displacement at any moment.

Q. The graph between $\sqrt{E_k}$ and $\frac{1}{P}$ is
$(E_k$ = kinetic energy and $P=$ linear momentum)

1. 
2. 
3. 
4. 

Q.

A car is moving along a straight level road with constant speed. Then

1. the work done on the car is infinite.

2. the work done on the car is zero.

3. the work done on the car is a measure of the gravitational potential energy.

4. the work done on the car cannot be found.

Q. The initial velocity $v_1$ required to project a body vertically upward from the surface of the earth to just reach a height of $10R$, where $R$ is the radius of the earth, may be described in terms of escape velocity $v_e$ such that $v_i=\sqrt{\frac{x}{y}}\times v_e$.The value of $x$ will be_______.

Q.

Two solids A and B of mass $1kg$ and $2kg$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $\frac{K{E}_A}{K{E}_B}$ will be $\frac{A}{1}$. So the value of $A$ will be ________.

Q. A body of mass $2\text{kg}$ is moving uniformly with the velocity of $2\hat{i}+3\hat{j}+4\hat{k}$. Find its kinetic energy.

1. $21\text{J}$
2. $25\text{J}$
3. $37\text{J}$
4. $29\text{J}$

Q. A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by $2\text{m/s}$ and the boy changes his speed by $x\text{m/s}$ so that the kinetic energies of the boy and the man are again equal. Then $x$ in $\text{m/s}$ is

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

Q. Two blocks A and B of mass 2kg and 4kg are placed one over other and the 2kg mass block is placed on 4kg block with initial velocity v. A time varying horizontal force F=2t is applied on the upper block. Draw a graph showing accelerations of A and B on y axis and time on x axis. Coefficients of friction between A and B is 1/2 and the horizontal surface over which B is placed is smooth. Take g=10m/s^2.

Q.

If the K.E. of a particle is doubled, then its momentum will

1. Remain unchanged

2. Be doubled

3. Be quadrupled

4. Increase $\sqrt{2}$ times

Q.

Two masses of 1 gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitudes of their linear moment is

1. 4 : 1

2. 1 : 2

3. 1 : 16

4. 

Q.

Work done by the resultant force is always equal to a change in kinetic energy.

1. True
2. False

Q.

Work energy theorem is valid in all inertial frames of references.

1. True
2. False

Q. If the speed of a vehicle increases by $2\text{m/s}$, its kinetic energy is doubled, then original speed of the vehicle is

1. $\sqrt{2}+1\text{m/s}$
2. $2(\sqrt{2}-1)\text{m/s}$
3. $\sqrt{2}(\sqrt{2}+1)\text{m/s}$
4. $2(\sqrt{2}+1)\text{m/s}$

Q.

When can one use the work energy theorem?

Q. A particle of mass $m$ has half the kinetic energy of another particle of mass $\frac{m}{2}$. The ratio of the speeds of the lighter and heavier particles is

1. $1:1$
2. $1:2$
3. $2:1$
4. $1:4$