Work Energy Theorem Application

Q.

A particle of mass m moves with a variable velocity v, which changes with distance covered x along a straight line as $v=k\sqrt{x}$, where k is a positive constant . The work done by all the forces acting on the particle, during the first t second is

1. $\frac{m{k}^4}{t^2}$

2. $\frac{m{k}^4{t}^2}{4}$

3. $\frac{m{k}^4{t}^2}{8}$

4. $\frac{m{k}^4{t}^2}{16}$

Q. A time varying force $F=10\sqrt{2}t$ starts acting on the $3\text{kg}$ block kept on a rough horizontal surface $(\mu =0.2)$ at $t=0$. Find the time when the horizontal motion begins.
(Take $g=10{\text{m/s}}^2$)

1. $\frac{7}{2}\text{s}$
2. $\frac{3}{2}\text{s}$
3. $\frac{1}{2}\text{s}$
4. $\frac{5}{2}\text{s}$

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. A rifle bullet loses ${\frac{1}{20}}^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

1. 5
2. 10
3. 11
4. 20

Q. A roller coaster of mass $2000\text{kg}$ has a speed of $v_1=10\text{m/s}$ as it goes over the top of a $15\text{m}$ high hill. Then it goes over another hill of height $10\text{m}$ and at the crest of that hill, the roller coaster is moving with speed $v_2=13\text{m/s}$. How much is the work done by friction on the roller coaster during its movement between the hills ? Take $g=10{\text{m/s}}^2$.

1. $15500\text{J}$
2. $-15500\text{J}$
3. $-31000\text{J}$
4. $31000\text{J}$

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. The same

2. Doubled

3. Halved

4. Four times

Q. A block of mass $8\text{kg}$, moving in x-direction with a constant speed of $15\text{m/s}$, is subjected to a retarding force of $F=10x\text{N}$ during its travel from $x=10\text{m}$ to $x=15\text{m}$. Find its final kinetic energy.

1. $300\text{J}$
2. $325\text{J}$
3. $275\text{J}$
4. $350\text{J}$

Q.

The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of ${15}^{\circ }$ with the horizontal is

1. 4.36 kJ

2. 5.17 kJ

3. 8.91 kJ

4. 9.82 kJ

Q. A bullet leaving the muzzle of a rifle barrel with a velocity $v$ penetrated a plank and loses one-fifth of its velocity. It then strikes second plank, which it just penetrates through. Supposing the average resistance to the penetration is same in both the cases, the ratio of the thickness of the planks will be:

1. $\frac{9}{16}$
2. $\frac{1}{4}$
3. $\frac{1}{5}$
4. $\frac{9}{25}$

Q. A mass m slides down a plane inclined at an angle $\alpha$ to the horizontal. The height of the inclined plane is h and the coefficient of friction over both surface is $\mu$. Then the distance that it will move on the horizontal plane after covering the entire length of the inclined plane.

1. h- $\frac{h}{tan\alpha }$
2. $\frac{h}{\mu }$ - $\frac{h}{tan\alpha }$
3. $\frac{h}{\mu }$ - h
4. $\frac{h}{\mu }$ - $\frac{1}{tan\alpha }$

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. A block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed reduced to ${\frac{1}{3}}^{rd}$ of its original value. The spring constant of the spring is $\frac{8m{v}^2}{n{x}^2}.$ Find the value of $n$

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. 12 J

2. 18 J

3. 20 J

4. 16 J