Work and Energy Test

Result

Work and Energy Test - 55

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Weekly Quiz Competition

Question 1
1 / -0

If water is flowing in a pipe at a height 4m from the ground then its potential
energy per unit volume is (Reference is taken at ground, $$ g=10 \mathrm{m} / \mathrm{s}^{2} ) $$

A
$$

20 \mathrm{kJ} / \mathrm{m}^{3}

$$

B
$$

10 \mathrm{kJ} / \mathrm{m}^{3}

$$

C
$$

40 \mathrm{kJ} / \mathrm{m}^{3}

$$

D
$$

30 \mathrm{kJ} / \mathrm{m}^{3}

$$
Question 2
1 / -0

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $$t$$ is proportional to

A
$$

t^{1 / 2}

$$

B
$$

t^{3/ 4}

$$

C
$$

t^{3/ 2}

$$

D
$$

t^{2}

$$

Solution
Question 3
1 / -0

If a body is released from a certain height, during its fall.

A
Its kinetic energy increases and potential energy decreases.

B
Its potential energy increases and kinetic energy decreases.

C
Both potential and kinetic energy of that body increase

D
Both potential and kinetic energy of the body decrease

Solution
Question 4
1 / -0

When the force and the displacement are in the opposite directions, the work done by the force is ..........

A
$$positive$$

B
$$negative$$

C
$$zero$$

D
$$not form this$$

Solution

Work done by the force,
$$W=\vec F.\vec r=Frcos\theta$$. . . . . . . .(1)
If the force and the displacement are in the opposite direction, then angle between the force and the displacement is $$180^0$$
$$cos\theta=cos180^0=-1$$
from equation (1),
$$W=-Fr$$
The work done by the force is negative.
The correct option is B.
Question 5
1 / -0

A machine delivering constant power moves a body along straight line starting from rest. The distance moved by the body in time $$t$$ is proportional to

A
$$t^{3/4}$$

B
$$t^{3/2}$$

C
$$\sqrt t$$

D
$$t$$

Solution

Let the force applied on the body be $$F$$ and the distance travelled by it be $$s$$.
We know that power $$P=\dfrac{work}{time}$$

$$P=\dfrac{Fs}{t}=F \times \dfrac{s}{t}$$
Speed $$v=\dfrac{Distance \ 's'}{Time \ 't'}$$

So power $$P=Fv$$
The power delivered by the machine is constant.
$$\therefore P=Fv=constant \ 'k'$$ . . . (i)

By Newton's second law $$Force \ 'F'=mass \ 'm' \times acceleration \ 'a'$$
$$\Rightarrow F=ma$$ . . . (ii)

By first equation of motion $$v=u+at$$
$$\Rightarrow v=at$$ . . . (iii)
($$\because u=0$$ as body starts from rest)

Using $$(ii)$$ and $$(iii)$$ in $$eq. (i)$$
$$Fv=k$$
$$(ma)(at)=k$$
$$a^2=\dfrac{k}{mt}$$
$$\Rightarrow a=\sqrt{\dfrac{k}{mt}}=\left( \dfrac{k}{mt}\right)^{\frac{1}{2}}$$ . . . (iv)

From second equation of motion,
$$s=ut+\dfrac{1}{2}at^2$$
$$\Rightarrow s=\dfrac{1}{2}at^2$$ . . . (v)

By substituting value of $$a$$ from $$(iv)$$ in $$(v)$$
$$s=\dfrac{1}{2} \left( \dfrac{k}{mt}\right)^{\frac{1}{2}}t^2 $$

$$s=\dfrac{1}{2} \left( \dfrac{k}{m}\right)^{\frac{1}{2}} \left( \dfrac{1}{t}\right)^\frac{1}{2} t^2 $$

$$s=\left[ \dfrac{1}{2} \left( \dfrac{k}{m}\right)^{\frac{1}{2}} \right] (t)^{-1/2} (t)^2 $$

The quantity in the square brackets $$[ \ ]$$ is constant so
$$s \propto (t)^{-1/2} (t)^2 $$

$$s \propto t^{\frac{-1}{2}+2}$$

$$s \propto t^{3/2}$$

So option $$(B)$$ is the answer.
Question 6
1 / -0

A ball of mass 2 kg hits a floor with a speed of 4 m/s at an angle of $$ 60 ^o $$ with the normal.
If (e=1/2); then the change in the kinetic energy of the ball is

A
-6J

B
-12J

C
-9J

D
-3J

Solution
Question 7
1 / -0

From an automatic gun a man fires 360 bullets per minute with a speed of 360 km/hr. If each bullet weighs 20g, the power of the gun is

A
600 W

B
300 W

C
150 W

D
75 W

Solution

Power of gun = $$ \dfrac { \text{Total K.E. of fired bullet} }{ \text{time }} $$

Total KInetic Energy $$=n\times \dfrac{1}{2}mv^2$$

$$P = \dfrac {n \times \dfrac {1}{2}mv^2 }{t} = \dfrac {360}{60} \times \dfrac { 1}{2} \times 2 \times 10^{-2} \times ( 100)^2 = 600 W $$
Question 8
1 / -0

A body of mass 200 g moving on a test has final K.E. of 50 J after travelling a distance of 10 cm. Assuming 90% loss of energy due to friction. The initial speed of the body is

A
10 $$ms^{-1}$$

B
$$10\sqrt{50}ms^{-1}$$

C
$$5\sqrt{50}ms^{-1}$$

D
$$50\sqrt{50}ms^{-1}$$

Solution
Question 9
1 / -0

Potential energy v/s displacement curve for one dimensional conservative field is shown. Force at A and B is respectively -

A
Positive, Positive

B
Positive, Negative

C
Negative, Positive

D
Negative, Negative

Solution
Question 10
1 / -0

A block of mass $$20 kg$$ is being brought down by a chain. If block acquires a speed of $$2 m/s$$ in dropping down $$2 m$$. Find work done by the chain during the process. ($$g= 10m/s^{2}$$ )

A
$$-360 J$$

B
$$400 J$$

C
$$360 J$$

D
$$-280 J$$

Solution