The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at

(1) C

(2) B

(3) B and C

(4) A and D

Figure shows the F-x graph. Where F is the force applied and x is the distance covered by the body along a straight line path. Given that F is in newton and x in metre, what is the work done ?

(1) 10 J

(2) 20 J

(3) 30 J

(4) 40 J

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length, the line OA will

(1) Shift towards F-axis

(2) Shift towards X-axis

(3) Remain as it is

(4) Become double in length

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)

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) ?

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

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

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

(d) \(\left(2 t + 3 t^{3}\right) W\)