The graph between \(E\) and \(v\) is:

1.		2.
3.		4.

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?

1. 

2.

3. 

4. 

The diagrams represent the potential energy U as a function of the inter-atomic distance r. Which diagram corresponds to stable molecules found in nature.

1. 

2. 

3. 

4. 

The relationship between the force F and the position x of a body is as shown in the figure. The work done in displacing the body from x = 1 m to x = 5 m will be:

A particle is placed at the origin and a force F = kx is acting on it (where k is positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function) 

1. 

2. 

3. 

4. 

A spring of force constant k is cut into lengths of ratio 1:2:3. They are connected in series and the new force constant is $k^{\text{'}}$. If they are connected in parallel and force constant is $k^{\text{'}\text{'}}, then k^{\text{'}}:k^{\text{'}\text{'}}$ is 

1. 1:6

2. 1:9

3. 1:11

4. 6:11

Consider a drop of rain water having mass \(1\) g falling from a height of \(1\) km. It hits the ground with a speed of \(50\) m/s.  Take \(g\) constant with a value of \(10\) m/$s^2$.  The work done by the 
(i) gravitational force and the (ii) resistive force of air is:

Two identical balls \(\mathrm{A}\) and \(\mathrm{B}\) having velocities of \(0.5~\text{m/s}\) and \(-0.3~\text{m/s}\) respectively collide elastically in one dimension. The velocities of \(\mathrm{B}\) and \(\mathrm{A}\) after the collision respectively will be:
1. \(-0.5 ~\text{m/s}~\text{and}~0.3~\text{m/s}\) 
2. \(0.5 ~\text{m/s}~\text{and}~-0.3~\text{m/s}\)
3. \(-0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}\)
4. \(0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}\)

A body of mass 1 kg begins to move under the action of a time dependent force \(F = 2 t\) \(\hat{i} + 3 t^{2}\ \hat{j}\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along X and Y axis, What power will be developed by the force at the time (t) ?

1. \(\left(2 t^{2} + 4 t^{4}\right) W\)         

2. \(\left(2 t^{3} + 3 t^{4}\right) W\)

3. \(\left(2 t^{3} + 3 t^{5}\right) W\)         

4. \(\left(2 t + 3 t^{3}\right) W\)