Work Energy and Power Test

Result

Work Energy and Power Test - 77

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Question 1
1 / -0

A particle moves along x-axis under the action of a position dependent force $$ F= (5x^2-2x) N $$. work done by forces on the particle when it moves from origin to x=3 m is

A
45J

B
36j

C
32J

D
42J

Solution
Question 2
1 / -0

A particle of mass 2kg is moving in a circular path of radius 1m with a speed that varies with time as $$v=(t^2-t)m/s$$. The force acting on the particle at t=2s is

A
8N

B
6N

C
10N

D
5N

Solution
Question 3
1 / -0

A block of mass m is connected rigidly with a smooth plank by a light spring of stiffness K. If the plank is moved with constant velocity $${ \upsilon }_{ 0 }$$, find the work done by the external agent till the maximum compression of the spring.

A
$$\dfrac { 1 }{ 2 } { mu }_{ 0 }^{ 2 }$$

B
$$\frac { 3 }{ 4 } { mu }_{ 0 }^{ 2 }$$

C
$${ mu }_{ 0 }^{ 2 }$$

D
$$\dfrac { 3 }{ 2 } { mu }_{ 0 }^{ 2 }$$

Solution

Let work done by spring and external agent be $$W_{s}$$ and $$W_{e} $$ respectively.

At the time of maximum compression, the velocity of block will be equal to velocity of plank i.e $$v_0$$.

So, $$\Delta K = \dfrac{1}{2}mv_0^2$$ (because plank's velocity did not change)

Now, from the reference of plank

Work done by Spring $$(W_s)$$= Change in Kinetic Energy of block

$$ W_s = 0- \dfrac{1}{2}mv_0^2$$

$$\Rightarrow W_s = -\dfrac{1}{2}mv_0^2$$

On Applying Work-Energy theorem on whole system from the reference of ground, we have

$$W_{e}+ W_s = \Delta K$$

$$\Rightarrow W_{e} -\dfrac{1}{2}mv_0^2 = \dfrac{1}{2}mv_0^2-0$$

$$ \Rightarrow W_{e} = \dfrac{1}{2}mv_0^2 + \dfrac{1}{2}mv_0^2$$

$$ = mv_0^2$$

So, the correct option will be $$(C)$$
Question 4
1 / -0

A particle is moving in a force field given by F $$=$$ $${y^2}i - {x^2}j$$. starting from A, the particle has to reach C either along ABC or ADC. Let the work done along the two paths be $${W_1}$$ and $${W_2}$$ respectively. Then ($${W_1}$$,$${W_2}$$) are

A
$$(-1,1)$$

B
$$(1,0)$$

C
$$(1,1)$$

D
$$(-1,-1)$$

Solution
Question 5
1 / -0

A heavy particle hanging from a fixed point by a light inextensible string of length l h projected horizontally with a speed of $$\sqrt { { g }^{ l } } $$. Find the speed of the particle and the inclination of the string to the vertical at the instant of the motion, when the tension in the string is equal to the weight of the particle.

A
$$\sqrt { gl } $$

B
$$\sqrt { 2gl } $$

C
$$\sqrt { 3gl } $$

D
$$\sqrt { \frac { gl }{ 3 } } $$

Solution
Question 6
1 / -0

The distance x moved by a body of mass 0.5 kg by a force varies with time as $$ x = 3t^2 + 4t + 5 $$, x is expressed in meter and t is seconds. The work done by force in first 2 seconds.

A
75 J

B
50 J

C
60 J

D
100 J
Question 7
1 / -0

A strign of length $$1=1m$$ is fixed at one end and carries a mass of $$100gm$$ at other end. The string makes $$\sqrt { 5 } \pi$$ revolutions per second about a vertical axis passing through its second end. What is the angle of inclination of the string with the vertical?

A
$$30^0$$

B
$$45^0$$

C
$$60^0$$

D
$$75^0$$

Solution
Question 8
1 / -0

A body of mass m is moved up the plane of varying slope by a tangential force up to height h.The coefficient of friction between the surface and the block is $$\mu $$.
1.The work done on the block.

A
by gravity depends upon the height h

B
by gravity depends upon the force F

C
by friction depends upon the speed of block.

D
by friction is $$\mu $$mgx, when moved slowly.

Solution
Question 9
1 / -0

The displacement time graph of a uniformed accelerating body of mass 2 kg. initially at rest is shown below the magnitude of force acting on the body is

A
$$0.5 N$$

B
$$1 N$$

C
$$2 N$$

D
$$4 N$$

Solution
Question 10
1 / -0

Two bodies A and B have masses $$20\ kg$$ and $$5\ kg$$ respectively . Each one is acted upon by a force of $$4\ kg.-wt$$. If they acquire the same kinetic energy in times $$t_{ A }\ and\ t_{ B }$$, then the ratio $$\dfrac { t_{ A } }{ t_{ B } } $$:

A
$$\dfrac { 1 }{ 2 } $$

B
$$2$$

C
$$\dfrac { 2 }{ 5 } $$

D
$$\dfrac { 5 }{ 6 } $$

Solution