Two inclined frictionless tracks, one gradual and the other steep meet at \(A\) from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

        
Which of the following statement is correct?

1.	Both stones reach the bottom at the same time but not at the same speed.
2.	Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.
3.	Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
4.	Both stones reach the bottom at different times and at different speeds.

The potential energy function for a particle executing linear SHM is given by \(V \left(\right. x \left.\right) = \dfrac{1}{2} kx^{2}\) where \(k\) is the force constant of the oscillator (Fig). For \(k = 0.5~\text{N/m},\) the graph of \(V~(x)\) versus \(x\) is shown in the figure. A particle of total energy \(E\) turns back when it reaches \(x = \pm \left(x \right)_{m}.\) If \(V\) and \(K\) indicate the \(PE\) and \(KE,\) respectively of the particle at \(x = + \left(x \right)_{m}, \) then which of the following is correct?

              

1. \(V = 0, K = E\)
2. \(V = E, K = 0 \)
3. \(V < E, K = 0\)
4. \(V = 0, K, E\)

Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same time moving initially with a speed \(v\) as shown in the figure.

      
If the collision is elastic, which of the following (as depicted in the figure) is a possible result after collision?

1.		2.
3.		4.

A body of mass \(0.5~\text{kg}\) travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\text{m}^{-1/2}\text{s}^{-1}\). The work done by the net force during its displacement from \(x=0~\text{m}\) to \(x=2~\text{m}\) is:
1. \(15~\text{J}\)
2. \(50~\text{J}\)
3. \(10~\text{J}\)
4. \(100~\text{J}\)

Two blocks \(M_1\)​ and \(M_2\)​ having equal mass are free to move on a horizontal frictionless surface. \(M_2\)​ is attached to a massless spring as shown in figure. Initially, \(M_2​\) is at rest and \(M_1​\) is moving toward \(M_2\)​ with speed \(v \) and collides head-on with \(M_2.\) 

      
Consider the following given statements:

During an inelastic collision between two bodies, which of the following quantities always remain conserved?

A body is falling freely under the action of gravity alone in a vacuum. Which of the following quantities remain constant during the fall?

A bicyclist comes to a skidding stop in \(10~\text m.\) During this process, the force on the bicycle due to the road is \(200~\text N\) is directly opposed to the motion. The work done by the cycle on the road is:
1. \(+2000~\text J\)
2. \(-200~\text J\)
3. zero
4. \(-20000~\text J\)

A man squatting on the ground gets straight up and stands. The force of reaction of the ground on the man during the process is