Work Energy and Power Test

Result

Work Energy and Power Test - 58

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Weekly Quiz Competition

Question 1
1 / -0

Two bodies traveling with velocity $$20ms^{-1}$$ and $$40ms^{-1}$$ have same K.E. If the mass of the body having velocity $$40ms^{-1}$$ is 8 kg the mass of other body is

A
8 Kg

B
16 kg

C
24 kg

D
32 kg

Solution

Given
$$ V_1 = 20 m/s$$ and $$ V_2 = 40 m/s$$
$$ M_2 = 8\ kg $$

$$K.E_1 = K.E_2$$
$$\dfrac{1}{2}M_1V_1^2 = \dfrac{1}{2}M_2V_2^2 $$
$$\implies M_1 = M_2 \times \dfrac{V_2^2}{V_1^2} = 8\times \dfrac{40^2}{20^2} = 32\ kg$$
Question 2
1 / -0

A body of mass 2$$\mathrm { Kg }$$ moving (initially) with 10$$\mathrm { m } / \mathrm { s }$$ is acting upon by a resultant constar which is opposite to its initial velocity. Its speed decreases to 4$$\mathrm { m } / \mathrm { s }$$ in 1 s. Then the force

A
12$$N$$

B
28$$N$$

C
8$$N$$

D
none
Question 3
1 / -0

A body of mass 1 kg falls from rest through the air, a distance of 200 m and acquires a speed 50 m/s. Work done against air friction is

A
$$750 J$$

B
$$1250 J$$

C
$$1960 J$$

D
$$3210 J$$

Solution
Question 4
1 / -0

A block of mass m is oscillating on smooth between two light springs of spring constant K separated by a distance I colliding elastically with the spring.If the velocity of the blocks is increased by an external impulse when it is not touching either of the spring then time period.

A
Increases

B
Decreases

C
Remain same

D
Time period is independent of I
Question 5
1 / -0

A perfectly elastic ball falls on a horizontal floor from a height in a time $$t$$. It will hit the floor again after a time $$t'$$. The ratio of $$t'$$ and t is

A
$$1:1$$

B
$$1:2$$

C
$$2:1$$

D
$$1:4$$
Question 6
1 / -0

As shown in figure, ball of of mass $$m \,kg$$ is suspended by a string $$\ell \,cm$$ long. Keeping the string always taut, the ball describes a horizontal circle of radius $$\dfrac{\ell}{2}$$. Calculate the angular speed.

A
$$\sqrt{\dfrac{2g}{3\ell}}$$

B
$$\sqrt{\dfrac{2g}{\sqrt{3}\ell}}$$

C
$$\sqrt{\dfrac{3g}{2\ell}}$$

D
None of these

Solution

Let $$\theta$$ be the angle made by the string and with the vertical
$$\implies tan \theta= \dfrac1 {\sqrt{3}}$$
Let $$T$$ be the tension in the string and $$\omega $$ is the angular speed.

From Free Body Diagram
$$T cos \theta =mg$$
$$T sin \theta =m\omega^2 \dfrac l2 $$

Form above two equations we get

$$\omega =\sqrt{\dfrac{2tan \theta g}{l}}$$
using the value of $$ tan \theta $$

Angular speed , $$\omega= \sqrt{\dfrac{2 g}{\sqrt{3}l}}$$
Question 7
1 / -0

A man of mass 20 kg is running in a straight line with velocity 10 m/s. What is value of his kinetic energy?

A
$$10\ J$$

B
$$100\ J$$

C
$$1000\ J$$

D
$$10000\ J$$

Solution

The kinetic energy of the particle is given as-
$$K.E. = \dfrac{1}{2}mv^2$$
$$m$$; mass of the object
$$v$$; speed of the object
$$\Rightarrow K.E. = \dfrac{1}{2} \times 20 \times 10^2J$$
$$\Rightarrow K.E. = 1000 J$$
Question 8
1 / -0

A body of mass $$8\ kg$$ collides elastically with a stationary mass of $$2\ kg$$. If initial $$KE$$ of moving mass be $$E$$, the kinetic energy left with it after the collision will be:

A
$$0.80\ E$$

B
$$0.64\ E$$`

C
$$0.36\ E$$

D
$$0.08\ E$$

Solution
Question 9
1 / -0

A rubber band of length $$\lambda$$ has a stone of mass $$m$$ tied to its one end. It is whirled with speed $$v second$$ that the stone described a horizontal circular path. The tension $$T$$ in the rubber band is -

A
zero

B
$$mv^2/\lambda $$

C
$$>(mv^2)/\ell $$

D
none

Solution

As there is only Tension T is theonly force. So it is the necessary centripetal force
$$T= \dfrac{mv^2}{\lambda}$$
Question 10
1 / -0

A ball of mass $$m_{1}$$ is moving with velocity $$v$$. It collides head on elastically with a stationary ball of mass $$m_{2}$$. The velocity of ball becomes $$\dfrac{v}{3}$$ after collision, then the value of the ratio $$\dfrac{m_{2}}{m_{1}}$$ is:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution