The length of a spring is \(l_1\) and \(l_2\) when stretched with a force of \(4\) N and \(5\) N respectively. Its natural length is?

1.	\(l_2+l_1\)	2.	\(2(l_2-l_1)\)
3.	\(5l_1-4l_2\)	4.	\(5l_2-4l_1\)

Two springs with spring constants $k_1$ = 1500 N/m and $k_2$ = 3000 N/m are stretched by the same force. The ratio of potential energy stored in the springs will be 

1. 2:1

2. 1:2

3. 4:1

4. 1:4

A block of mass 2 kg moving with velocity of 10 m/s on a smooth surface hits a spring of force constant $80\times {10}^3$ N/m as shown. The maximum compression in the spring is

1. 5 cm

2. 10 cm

3. 15 cm

4. 20 cm

A particle of mass 10 kg is moving with velocity of $10\sqrt{x}$ m/s, where x is displacement . The work done by net force during the displacement of particle from x = 4 to x = 9 m is 

1. 1250 J

2. 1000 J

3. 3500 J

4. 2500 J

A body starts moving from rest in straight line under a constant power source. Its displacement in time t is proportional to

1. $t^{1/2}$

2. t

3. $t^{3/2}$

4. $t^2$

A block of mass m = 25 kg on a smooth horizontal surface with a velocity $\overrightarrow{v}$ =3 $m{s}^{-1}$ meets the spring of spring constant k = 100 N/m fixed at one end as shown in the figure. The maximum compression of the spring and velocity of the block as it returns to the original position respectively are: 

1.  1.5 m, -3 $m{s}^{-1}$

2.  1.5 m, 0 $m{s}^{-1}$

3.  1.0 m, 3 $m{s}^{-1}$

4.  0.5 m, 2 $m{s}^{-1}$

The velocity, given to the block of mass (m), is $\sqrt{\frac{7}{2}gl}<mspace\; width="1em"></mspace>$to rotate it in a circle of radius l. Calculate the height (h) where the block leaves the circle.

1. $\frac{3l}{2}$

2. $\frac{4l}{3}$

3. $\frac{5l}{4}$

4. None of these

If length of string is $l\mathit{\hspace{0.17em}}\mathit{=}\mathit{\hspace{0.17em}}\frac{\mathit{10}}{\mathit{3}}m\mathit{,}\mathit{\hspace{0.17em}}\frac{{\mathit{T}}_{\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{T}}_{\mathit{m}\mathit{i}\mathit{n}}}\mathit{=}\mathit{4}$

$\mathrm{where}$
$<mspace\; width="1em"></mspace>{\mathrm{T}}_{\max }=<mspace\; width="1em"></mspace>\mathrm{Maximum}<mspace\; width="1em"></mspace>\mathrm{tension}<mspace\; width="1em"></mspace>\mathrm{in}<mspace\; width="1em"></mspace>\mathrm{the}<mspace\; width="1em"></mspace>\mathrm{string}$
${\mathrm{T}}_{\min }=M\mathrm{inimum}<mspace\; width="1em"></mspace>\mathrm{tension}<mspace\; width="1em"></mspace>in<mspace\; width="1em"></mspace>\mathrm{the}<mspace\; width="1em"></mspace>\mathrm{string}.$
$\mathrm{Velocity}<mspace\; width="1em"></mspace>\mathrm{at}<mspace\; width="1em"></mspace>\mathrm{highest}<mspace\; width="1em"></mspace>\mathrm{point}<mspace\; width="1em"></mspace>\mathrm{is}<mspace\; width="1em"></mspace>-$

1.  10 m/s

2.  20 m/s

3.  $\frac{10}{\sqrt{2}}\mathrm{m}/\mathrm{s}$

4.  $10\sqrt{3}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

The relation between velocity (v) and time (t) is $v\propto \sqrt{\mathrm{t}}$, then which one of the following quantity is constant?

1.  Force

2.  Power

3.  Momentum

4.  Kinetic Energy

A particle is moving on the circular path of the radius (R) with centripetal acceleration $a_c=k^{2}R{t}^2$. Then the correct relation showing power (P) delivered by net force versus time (t) is 

1. 1

2. 2

3. 3

4. 4