A spring \(40~\text {mm}\) long is stretched by the application of a force. If \(10 ~\text{N}\) force required to stretch the spring through \(1 ~\text{mm,}\) then work done in stretching the spring through \(40 ~\text{mm}\) is

1. \(84~\text{J}\)

2. \(68~\text{J}\)

3. \(23~\text{J}\)

4. \(8~\text{J}\)

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

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

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

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

A body is displaced from (0,0) to (1m,1m) along the path x=y by a force $F=\left(x^2\hat{j}+y\hat{i}\right)N$. The work done by this force will be :

1. $\frac{4}{3}J$

2. $\frac{5}{6}J$

3. $\frac{3}{2}J$

4. $\frac{7}{5}J$

A weightless rod of length 2l carries two equal mass 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in a vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in the horizontal position. The speed of the mass B at the instant rod becomes vertical is:

1. \(\sqrt{\frac{3 g l}{5}} \)

2. \(\sqrt{\frac{4 g l}{5}} \)

3. \(\sqrt{\frac{6 g l}{5}} \)

4. \(\sqrt{\frac{7 g l}{5}} \)

A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be

1.  ${\mathrm{Fv}}^2$

2.  Fv

3.  $\mathrm{F}/{\mathrm{v}}^2$

4.  F/v