Defining Kinetic Energy

Q.

The kinetic energy of an object of mass, m moving with a velocity of $5{\mathrm{ms}}^{-1}$ is $25\mathrm{J}$, What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?

Q.

Two masses of $M$ and $4M$ are moving with equal kinetic energy. The ratio of their linear momentum is

1. $1:8$

2. $1:4$

3. $1:2$

4. $4:1$

Q.

If the speed of the body is halved, what will be the change in its K.E.?

Q.

A motorcycle and a bus are moving with the same momentum which of them has greater kinetic energy?

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. As shown in diagram there are five identical rods. Length of each rod is $l$ and mass $m$. Find out distance of $\text{C.O.M.}$ of system From $\left(C\right)$

Q. Kinetic energy is the energy possessed by a body by the virtue of its motion.

1. False
2. True

Q. A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be

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

Q.

For the same value of kinetic energy, the momentum shall be maximum for

1. a proton

2. an electron

3. a deutron

4. an $\alpha -particle$

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

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

Q. Two bodies of masses $3\text{kg}$ and $6\text{kg}$ possess kinetic energies of $6\text{J}$ and $10\text{J}$ respectively. What is the ratio of their linear momentum?

1. $\sqrt{\frac{3}{10}}$
2. $\sqrt{\frac{3}{5}}$
3. $\sqrt{\frac{10}{3}}$
4. $\sqrt{\frac{5}{3}}$

Q.

All moving bodies possess _________.

Q.

Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momentum, then ratio $p_1:p_2$ is equal to

1. $m_1:m_2$

2. $m_2:m_1$

3. $\sqrt{m_1}:\sqrt{m_2}$

4. $m_1^2:m_2^2$

Q.

If the speed of the body is halved, what will be the change in its $K.E.?$

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

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

Q. A particle of mass m falling from height h reaches the ground with velocity $\sqrt{0.8gh}$. Work done by friction force on the particle is

h ऊँचाई से गिरता हुआ m द्रव्यमान का एक कण धरातल पर वेग $\sqrt{0.8gh}$ से पहुँचता है। कण पर घर्षण बल द्वारा किया गया कार्य है

1. –0.2mgh
   
2. –0.4mgh
   
3. –0.8mgh
   
4. –0.6mgh
   

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

Q. Three masses of $3\text{kg},4\text{kg}$ and $5\text{kg}$ respectively are having same kinetic energy. Which of these masses will move fastest?

1. $3\text{kg}$
2. $4\text{kg}$
3. $5\text{kg}$
4. All of these masses will have same speed

Q. Three masses of $3\text{kg},4\text{kg}$ and $5\text{kg}$ respectively are having same kinetic energy. Which of these masses will move fastest?

1. $3\text{kg}$
2. $4\text{kg}$
3. $5\text{kg}$
4. All of these masses will have same speed

Q. Figure shows two small blocks $A$ and $B$ placed on a smooth horizontal surface. They start moving from the same line with force $2F$ and $F$ respectively acting on the blocks. Their momentum and kinetic energies at the instants of crossing the finishing line as shown in figure are $p_A,p_B$ and $K_A,K_B$. Then, choose the correct option.

1. $K_A=K_B,p_A=p_B$
2. $K_A>K_B,p_A>p_B$
3. $K_A>K_B,p_A<p_B$
4. $K_A>K_B,p_A=p_B$

Q. A small ball is rolled with speed $u$ from point $A$ along a smooth circular track as shown in figure. If $x=3R$, then determine the point of projection after passing through $C$, the highest point.

1. $\frac{3}{2}\sqrt{gR}$
2. $\frac{1}{2}\sqrt{gR}$
3. $\frac{5}{3}\sqrt{gR}$
4. $\frac{5}{2}\sqrt{gR}$

Q.

What happens to the kinetic energy of an object if its velocity is doubled? Explain.

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. $\sqrt{2}:1$

3. 1 : 2

4. 1 : 16

Q.

The momentum of a body increases by 20%. Then the percentage increase in its kinetic energy is

1. $36$

2. $44$

3. $52$

4. $60$

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.

When velocity is halved, its kinetic energy becomes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\text{th}$.

1. True
2. False

Q. The linear momentum of the 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 having a momentum of $3\mathrm{î}+5\mathrm{ĵ}+\sqrt{15}\mathrm{k̂}$ and is having a mass of $\frac{7}{4}$kg. Determine the kinetic energy of ball.