Work Energy Theorem

Q.

Work done by the force of gravity, when a body is lifted to height h above the ground is :

1. zero

2. positive

3. negative

4. none of these

Q.

For the given cell:

$$\begin{gathered} \mathrm{Cu}\left(\mathrm{s}\right)\left|{\mathrm{Cu}}^{2+}\right({\mathrm{C}}_1\mathrm{M}\left)\right|\left|{\mathrm{Cu}}^{2+}\right({\mathrm{C}}_2\mathrm{M}\left)\right|\mathrm{Cu}\left(\mathrm{s}\right) \\ \mathrm{Change}\mathrm{in}\mathrm{Gibbs}\mathrm{energy}\left(\mathrm{\Delta G}\right)\mathrm{is}\mathrm{negative},\mathrm{if}: \end{gathered}$$

1. ${\mathrm{C}}_2=\sqrt{2}{\mathrm{C}}_1$

2. ${\mathrm{C}}_2={\mathrm{C}}_1\sqrt{2}$

3. ${\mathrm{C}}_1=2{\mathrm{C}}_2$

4. ${\mathrm{C}}_1={\mathrm{C}}_2$

Q.

Establish the relationship between the kinetic energy and the momentum of the body.

Q.

A bullet is fired from a gun. Which will have greater kinetic energy: the bullet or the gun?

Q. A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is

1. $mgx$
2. $-mgy$
3. $-mg(x+y)$
4. $mg(x-y)$

Q. A pendulum of mass $m$ and length $l$ is suspended from the ceiling of a trolley which has a constant acceleration $a$. The maximum deflection $\theta$ of the pendulum from the vertical is

1. ${\tan }^{-1}\left(\frac{a}{g}\right)$
2. ${\tan }^{-1}\left(\frac{2a}{g}\right)$
3. $2{\tan }^{-1}\left(\frac{a}{g}\right)$
4. ${\tan }^{-1}\left(\frac{a}{g}\right)$

Q. A body of mass $2\text{kg}$ starts from rest, uniformly accelerates from the point $(1,2,3)$ to point $(2,3,5)$ in $3$ seconds. The net work done by the body in $3$ seconds is

1. $\frac{3}{4}\text{J}$
2. $\frac{2}{3}\text{J}$
3. $\frac{4}{9}\text{J}$
4. $\frac{9}{16}\text{J}$

Q. A projectile has the maximum range, if the angle of projection is

1. 0 degree
2. 30 degrees
3. 45 degrees
4. 90 degrees

Q.

The kinetic energy possessed by a body of mass m moving with a velocity v is equal to $\frac{1}{2}m{v}^2$ , provided

1. The body moves with velocities comparable to that of light

2. The body moves with velocities negligible compared to the speed of light

3. The body moves with velocities greater than that of light

4. None of the above statement is correcst

Q. A disc of radius $2m$ and mass $100kg$ rolls on a horizontal floor. Its centre of mass has a speed of $20cm/s$. How much work is needed to stop it ?

1. $3J$
2. $30kJ$
3. $2J$
4. $1J$

Q. An object of mass $m$ is tied to a string of length $l$ and a variable force $F$ is applied on it which brings the string gradually to angle $\theta$ with the vertical. Find the work done by the force $F$. ( Assume initial and final kinetic energy to be zero)

1. $mgl(1-\sin \theta )$
2. $mgl\left(\sin \theta \right)$
3. $mgl\left(\cos \theta \right)$
4. $mgl(1-\cos \theta )$

Q. A ball of mass $m$ is thrown in air with speed $v_1$ from a height $h_1$ and it is at a height $h_2(>h_1)$ when its speed becomes $v_2$. Find the work done on the ball by the air resistance.

1. $mg(h_2-h_1)+\frac{1}{2}m(v_2^2-v_1^2)$
2. $mg(h_2+h_1)+\frac{1}{2}m(v_2^2-v_1^2)$
3. $mg(h_2-h_1)$
4. $\frac{1}{2}m(v_2^2-v_1^2)$

Q.

You are in a lift moving from the $3^{\mathrm{rd}}$ floor to the ${12}^{\mathrm{th}}$ floor, through a height H. If the elevator moves at a constant speed without stopping, what is the work performed on you by the elevator? Take your body mass as M.

Q. A body of mass $0.5\text{kg}$ travels in a straight line with velocity, $v=a{x}^{3/2},$ where $a=5{\text{m}}^{-1/2}{\text{s}}^{-1}.$ What is the work done by the net force during its displacement from $x=0$ to $x=2\text{m}$?

1. $30\text{J}$
2. $40\text{J}$
3. $20\text{J}$
4. $50\text{J}$

Q. In an ideal pulley particle system, mass $m_2(>m_1)$ is connected with a vertical spring of stiffness $k$. If mass $m_2$ is released from rest, when the spring is undeformed, find the maximum compression of the spring.

1. $x=\frac{2(m_2-m_1)g}{k}$
2. $x=\frac{2\left(m_2\right)g}{k}$
3. $x=\frac{2(m_2+m_1)g}{k}$
4. $x=\frac{(m_2-m_1)g}{k}$

Q. A ball of mass $m$ is thrown in air with speed $v_1$ from a height $h_1$ and it is at a height $h_2(>h_1)$ when its speed becomes $v_2$. Find the work done on the ball by the air resistance.

1. $mg(h_2-h_1)+\frac{1}{2}m(v_2^2-v_1^2)$
2. $mg(h_2+h_1)+\frac{1}{2}m(v_2^2-v_1^2)$
3. $mg(h_2-h_1)$
4. $\frac{1}{2}m(v_2^2-v_1^2)$

Q. A particle of mass $M$, starting from rest, undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, the average power delivered to the particle is

1. $\frac{M{V}^2}{T}$
2. $\frac{1}{2}\frac{M{V}^2}{T^2}$
3. $\frac{M{V}^2}{T^2}$
4. $\frac{1}{2}\frac{M{V}^2}{T}$

Q. A block of mass 4 kg is at rest on a frictionless horizontal surface. A horizontal force as a function of displacement as shown in graph acts on block. Speed of block when it has displaced by 6m is (Write two digits after the decimal point.)

Q. An uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $\left(\frac{L}{n}\right)$ th part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

1. $\frac{2MgL}{n^2}$
2. $nMgL$
3. $\frac{MgL}{n^2}$
4. $\frac{MgL}{2n^2}$

Q. For the block moving as shown in figure, maximum compression in the spring will be approximately:
[Take $g=10{\text{m/s}}^2,\sqrt{1552-40\sqrt{3}}\approx 38.50\&10+2\sqrt{3}\approx 13.5$ for calculation. Neglect the effect of corner]

1. $2.5\text{m}$
2. $3\text{m}$
3. $2.1\text{m}$
4. $2\text{m}$

Q. A block of mass $m$ is moving with an initial velocity $v_0$ towards a stationary spring of stiffness $k$ attached to the wall as shown. Find the maximum compression in the spring.

1. $v_0\sqrt{\frac{m}{k}}$
2. $v_0\sqrt{\frac{k}{m}}$
3. $2v_0\sqrt{\frac{m}{k}}$
4. $2v_0\sqrt{\frac{k}{m}}$

Q. An ice skier is sliding from a point $\text{A}$ as shown in the figure below. If the slider starts from rest and acceleration due to gravity is $10\text{m}/s^2$, then what is the velocity of the skier at point $\text{B}$.

1. $10\sqrt{5}\text{m/s}$
2. $10\sqrt{2}\text{m/s}$
3. $15\sqrt{5}\text{m/s}$
4. $20\sqrt{2}\text{m/s}$

Q. A $500\text{kg}$ car, moving with a velocity of $36{\text{kmh}}^{-1}$ on a straight road unidirectionally, doubles its velocity in one minute. The power delivered by the engine for doubling the velocity is

1. $750\text{W}$
2. $1050\text{W}$
3. $1150\text{W}$
4. $1250\text{W}$

Q. A block of mass $5\text{kg}$ is moving in x-direction with a constant speed of $10\text{m/sec}$. It is subjected to a retarding force $F=-0.2x\text{joule /metre}$ during its travel from $x=20\text{metre}$ to $x=30\text{metre}$. Its final kinetic energy will be

1. $200\text{joule}$
2. $475\text{joule}$
3. $375\text{joule}$
4. $400\text{joule}$

Q. A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is

1. $mgx$
2. $-mgy$
3. $-mg(x+y)$
4. $mg(x-y)$

Q. Two baseballs are fired into a pile of hay. If one has twice the speed of the other, how much farther does the faster baseball penetrate? (Assume that the force of the haystack on the baseballs is constant).

1. Four times as far
2. Two times as far
3. Same as the first one.
4. Eight times as far

Q. A bullet of mass $50\text{g}$ is fired horizontally into a wooden block of mass $10\text{kg}$. The bullet penetrates the wooden block and moves through a distance of $5\text{m}$ before coming to a stop within the block. If the initial speed of the bullet is $100\text{m/s}$, then what is the deceleration of the bullet? (Assume retarding force is uniform)

1. $250{\text{m/s}}^2$
2. $100{\text{m/s}}^2$
3. $500{\text{m/s}}^2$
4. $1000{\text{m/s}}^2$

Q. A stone with weight $W$ is thrown vertically upward into the air from ground level with initial speed $v_0$. If a constant force $f$ due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is

1. $h=\frac{v_0^2}{2g(1+\frac{f}{W})}$
2. $h=\frac{v_0^2}{2g(1-\frac{f}{W})}$
3. $h=\frac{v_0^2}{3g(1+\frac{f}{W})}$
4. $h=\frac{v_0^2}{2g(1+\frac{2f}{W})}$

Q. A stone of mass $1\text{kg}$ tied to a light inextensible string of length $L=\frac{10}{3}\text{m}$ is whirling in a circular path of radius $L$, in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension is $4$ and if $g$ is taken to be $10{\text{m/s}}^2$, the speed of the stone at the highest point of the circle is

1. $20\text{m/s}$
2. $10\sqrt{3}\text{m/s}$
   
3. $5\sqrt{2}\text{m/s}$
4. $10\text{m/s}$

Q. A body is displaced from position $A$ to position $B$. Kinetic and potential energies of the body at positions $A$ and $B$ are $K_A=70\text{J},U_A=-50\text{J},K_B=-20\text{J}$ and $U_B=30\text{J}$. Then:

1. Work done by conservative forces is $-80\text{J}$.
2. Work done by all the forces is $-90\text{J}$.
3. Work done by non-conservative forces is $-10\text{J}$.
4. Work done by all the forces is $-80\text{J}$.