A weight 'mg' is suspended from a spring. The energy stored in the spring is U. The elongation in the spring is:

1.  $\frac{2\mathrm{U}}{\mathrm{mg}}$

2.  $\frac{\mathrm{U}}{\mathrm{mg}}$

3.  $\frac{\sqrt{2}\mathrm{U}}{\mathrm{mg}}$

4.  $\frac{\mathrm{U}}{\sqrt{2}\mathrm{mg}}$

The energy required to accelerate a car from rest to 30 m/s is E. The energy required to accelerate the car from 30 m/s to 60 m/s will be:

The speed of a particle moving in a circular path decreases with time. The instantaneous power due to the force acting on it will be:
1. Positive
2. Negative
3. Zero
4. Maybe positive or negative

A body is obliquely projected from the horizontal ground. The magnitude of gravity's power delivered during its motion from the ground to the topmost point is:

      
1. \(50~\text{J}\)
2. \(100~\text{J}\)
3. \(25~\text{J}\)
4. Zero

A particle is suspended by a light rod of length l. The minimum speed at which the particle should be projected, so that it moves in a vertical circle, is:

According to the work-energy theorem, the change in kinetic energy of a body is equal to work done by:

1.  Non-conservative force on the particle

2.  Conservative force on the particle

3.  External force on the particle

4.  All the forces on the particle

A block is carried slowly up an inclined plane. If \(W_f\) is work done by the friction, \(W_N\)${\mathrm{}}_{}$ is work done by the reaction force, \(W_g\) is work done by the gravitational force, and \(W_{ex}\) is the work done by an external force, then choose the correct relation(s):
1. \(W _N +   W _f   +   W _g   +   W _{ex}   =   0\)
2. \(W _N   =   0\)
3. \(   W _f   +   W _{ex}   =    - W _g\)
4. All of these

The position of a particle \((x)\) varies with time \((t)\) as \(x = (t - 2)^2\), where \(x\) is in meters and \(t\) is in seconds. Calculate the work done during \(t=0\) to \(t=4\) s if the mass of the particle is \(100~\text{g}.\)
1. \(0.4~\text{J}\)
2. \(0.2~\text{J}\)
3. \(0.8~\text{J}\)
4. zero