Work Energy and Power Test

Result

Work Energy and Power Test - 57

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A body of mass m is rotating in a vertical circle of radius 'r' with critical speed. The difference in its K.E. at the top and the bottom is _____.

A
2mgr

B
4 mgr

C
6 mgr

D
3 mgr

Solution
Question 2
1 / -0

A spring of force constant $$800 N/m$$ has an extension of $$5 cm$$. The work done in extending it from $$5 cm$$ to $$15 cm$$ is :

A
$$16 J$$

B
$$8 J$$

C
$$32 J$$

D
$$24 J$$

Solution

The work done is stored as elastic potential energy in the spring.

It is given by

$$W = \dfrac12 \times k ( x_2^2 - x_1^2)$$

$$x_1 = 5\, cm$$

$$x_2 = 15\, cm$$

Force constant, $$k = 800 \,N/m = \dfrac{800}{100} N/cm = 8 N/cm$$

$$W = \dfrac 12 \times 8 ( 15^2- 5^2) = \dfrac 12 \times 8 ( 225 - 25) $$

$$= \dfrac 12 \times 8 \times 200 = 800 \,N cm$$

$$W = 800\, N cm = 8 \,N m = 8\, J$$

Therefore,

The work done in extending it from $$5\,cm$$ to $$15\,cm$$ is $$8\, J$$.
Question 3
1 / -0

A vertical spring of force constant $$100 N/m$$ is attached with a hanging mass of $$10 kg$$. Now an external force is applied on the same so that the spring is stretched by additional $$2m$$. The work done by the force is ($$g= 10 m/s^2$$)

A
$$200 J$$

B
$$400 J$$

C
$$450 J$$

D
$$600 J$$

Solution

Given,

Spring Constant, $$k=100\,N/m$$

Additional elongation, $$x=2\,m$$

Work done, $$W=\dfrac 12kx^2$$

$$=\dfrac 12\times 100\times 2^2=200\,J$$
Question 4
1 / -0

A cone filled with water is whirled in a vertical circle of radius 4 m. What will be the time period of rotation so that water does not fall ?

A
4 s

B
6 s

C
2 s

D
1 s

Solution
Question 5
1 / -0

Two springs of force constants $$ \mathrm{K}_{1} $$ and $$ \mathrm{K}_{2} $$ $$ \left(\mathrm{K}_{1}>\mathrm{K}_{2}\right) $$ are stretched by same force. If $$ \mathrm{W}_{1} $$ and $$ W_{2} $$ be the work done stretching the springs then

A
$$

W_{1}=W_{2}

$$

B
$$W
_1<W_2$$

C
$$

\mathrm{W}_{1}>\mathrm{W}_{2}

$$

D
$$

W_{1}=W_{2}=0

$$

Solution

As the force on both the springs is same, we have

$$F=k_1x_1=k_2x_2$$ .....(1)

Now, work done on first spring, $$W_1=\dfrac 12k_1x_1^2$$ .......(2)

Work done on second spring, $$W_2=\dfrac 12k_2x_2^2$$ ...(3)

On dividing equation (2) by (3), we get

$$\dfrac{W_1}{W_2}=\dfrac{\dfrac 12 k_1x_1^2}{\dfrac 12 k_2x_2^2}$$

Hence using equation (1), we get

$$\dfrac{W_1}{W_2}=\dfrac{F_{x1}}{F_{x_2}}=\dfrac{x_1}{x_2}=\dfrac{k_2}{k_1}$$

As $$k_1>k_2$$, therefore, we get,

$$W_1<W_2$$

Hence, more work is done on spring with spring constant $$k_2$$.
Question 6
1 / -0

At the instant speed of block is maximum, the magnitude of force exerted by spring on the block is

A
$$\dfrac{mg}{2}$$

B
$$mg$$

C
Zero

D
None of these

Solution
Question 7
1 / -0

In $$10 s$$, a body of $$6 kg$$ mass is dragged $$8 m$$ with uniform velocity across a floor by a steady force of $$20 N$$. The K.E of the body is:

A
$$2.92 J$$

B
$$0.92 J$$

C
$$1.92 J$$

D
$$0J$$

Solution
Question 8
1 / -0

If the kinetic Energy possessed by a man of $$50$$kg is $$625J$$, the speed of man is

A
$$5m{s^{ - 1}}$$

B
$$50m{s^{ - 1}}$$

C
$$0.5m{s^{ - 1}}$$

D
$$500m{s^{ - 1}}$$

Solution
Question 9
1 / -0

A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly- elastic collision with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value of m is/are :

A
1 kg only

B
1 kg , 9kg

C
1 kg, 6kg

D
6kg only

Solution
Question 10
1 / -0

Water is dragged from a well of hepth 30 m using bucket of weight 50kg with water If the weight of the rope is 0.4 kg per metre, the amount of work done is

A
18228J

B
16464J

C
14700J

D
11760J

Solution