Work Energy and Power Test

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Work Energy and Power Test - 71

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Question 1
1 / -0

A force of $$5N$$ acts on a $$15kg$$ body initially at rest. The work done by the force during the first second of motion of the body is:

A
$$5J$$

B
$$\cfrac{5}{6}J$$

C
$$6J$$

D
$$75J$$

Solution
Question 2
1 / -0

A chain is held on a frictionless table with $$L/4$$ hanging over. Knowing total mass of the chain is $$M$$ and total length is $$L$$, the minimum work required to pull hanging part back too the table is:

A
$$\cfrac{MgL}{16}$$

B
$$\cfrac{MgL}{8}$$

C
$$\cfrac{MgL}{32}$$

D
$$\cfrac{MgL}{24}$$

Solution
Question 3
1 / -0

The time period of a simple harmonic pendulum in a stationary train is $$T$$. The time period of a mass attached to a spring is also $$T$$. The train accelerates at the rate $$5 ms^{-2}$$. If the new time periods of the pendulum and spring be $$T_p$$ and $$T_s$$ respectively, then

A
$$T_p = T_s$$

B
$$T_p > T_s$$

C
$$T_p < T_s$$

D
Cannot be predicted

Solution
Question 4
1 / -0

A small solid sphere of mass $$m$$ is released from a point $$A$$ at a height $$h$$ above the bottom of a rough track as shown in the figure. If the sphere rolls down the track without slipping, its rotational kinetic energy when it comes to the bottom of track is

A
$$mgh$$

B
$$\cfrac{10}{7}mgh$$

C
$$\cfrac{5}{7}mgh$$

D
$$\cfrac{2}{7}mgh$$

Solution
Question 5
1 / -0

Select the incorrect option:-
($$\tau = torque, \,v = velocity, \,\omega = angular \,velocity, \, a_c = centripetal \, acceleration$$)

A
$$\vec \tau \times \vec \tau = 0$$

B
$$\vec v . \vec \omega = 0$$

C
$$ \vec \omega \times \vec v= 0$$

D
$$ \vec a_c \times \vec v= 0$$

Solution
Question 6
1 / -0

A worker lifts a $$20.0 kg$$ bucket of concrete from the ground up to the top of a $$20.0 m$$ tall building. What is the amount of work that the worker did in lifting the bucket?

A
$$3.92 kJ $$

B
$$400 J$$

C
$$ 560 kJ $$

D
$$ 4.08 J $$

Solution

Given:
The mass of the bucket $$m=20\ kg$$
The height of the building $$h=20\ m$$
$$\text{Work done by the worker} = \text{Potential energy of bucket at the top of the building}$$

$$\therefore W = mgh$$

$$\Rightarrow W = 20 \times 9.8 \times 20$$

$$\Rightarrow W = 3920\;{\rm{J}}$$

Thus, the required work done is $$3.92\;k{\rm{J}}$$
Question 7
1 / -0

A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force $$F$$ can do is: (Given that spring does not break)

A
$$\cfrac{{F}^{2}}{k}$$

B
$$\cfrac{{2F}^{2}}{k}$$

C
$$\infty$$

D
$$\cfrac{{7F}^{2}}{k}$$

Solution
Question 8
1 / -0

A bob of mass $$m$$ is attached at one end of a string of length $$\iota $$. Other end of the string is fixed point $$O$$. Bob is rotating in circular path of radius $$\iota $$ in horizontal plane about $$O$$ with constant speed $$v$$, as shown in the figure. The average force exerted by string on the bob during its:

A
half revolution will be $$\dfrac{mv^{2}}{\pi \iota }$$

B
half revolution will be $$\dfrac{2mv^{2}}{\pi \iota }$$

C
one fourth revolution will be $$\dfrac{\sqrt{2mv^{2}}}{\pi \iota }$$

D
one revolution will be zero

Solution
Question 9
1 / -0

The work done in extending a spring by $$x_0$$ is $$W_0$$. Find the work done in further extension $$x_0$$.

A
$$W=2W_0$$

B
$$W=3W_0$$

C
$$W=W_0$$

D
$$W=\frac{1}{3} W_0$$
Question 10
1 / -0

A solid sphere of mass $$4kg$$ and radius $$1m$$ is rotating about the given axis $$xx'$$ with angular velocity $$10rad/s$$ shown in figure. The $${K.E}_{rotation}$$ is given by

A
$$180J$$

B
$$200J$$

C
$$240J$$

D
$$280J$$

Solution