A moving block having mass \(m\) collides with another stationary block having a mass of \(4m.\) The lighter block comes to rest after the collision. When the initial velocity of the lighter block is \(v,\) then the value of the coefficient of restitution \((e)\) will be:

A body initially at rest and sliding along a frictionless track from a height \(h\) (as shown in the figure) just completes a vertical circle of diameter \(\mathrm{AB}= D.\) The height \({h}\) is equal to:

Three objects, \(A:\) (a solid sphere), \(B:\) (a thin circular disk) and \(C:\) (a circular ring), each have the same mass \({M}\) and radius \({R}.\) They all spin with the same angular speed about their own symmetry axes. The amount of work \(({W})\)required to bring them to rest, would satisfy the relation:

An electron falls from rest through a vertical distance \(h\) in a uniform and vertically upward-directed electric field \(E.\) The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest through the same vertical distance \(h.\) The fall time of the electron in comparison to the fall time of the proton is:
1. smaller
2.  \(5\) times greater
3.  \(10\) times greater
4. equal

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is \(20\text{ m/s}^2\) at a distance of \(5\text{ m}\) from the mean position. The time period of oscillation is:
1. \(2\pi \text{ s}\)
2. \(\pi \text{ s}\)
3. \(2 \text{ s}\)
4. \(1 \text{ s}\)

The electrostatic force between the metal plates of an isolated parallel plate capacitor \(C\) having a charge \(Q\) and area \(A\) is:

An electron of mass \(m\) with an initial velocity \(\overrightarrow v= v_0\hat i\)$\stackrel{}{}$\( ( v_o > 0 ) \) enters in an electric field \(\overrightarrow E = -E_0 \hat i\) \((E_0 = \text{constant}>0)\) at \(t=0.\) If \(\lambda_0,\)${\mathrm{}}_{}$ is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time \(t?\)

For radioactive material, the half-life is \(10\) minutes. If initially, there are \(600\) number of nuclei, the time taken (in minutes) for the disintegration of \(450\) nuclei is :
1. \(20\)
2. \(10\)
3. \(30\)
4. \(15\)

When the light of frequency \(2\nu_0\) (where \(\nu_0\) is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is \(v_1.\) When the frequency of the incident radiation is increased to \(5\nu_0,\) the maximum velocity of electrons emitted from the same plate is \(v_2.\) What will be the ratio of \(v_1\) to \(v_2?\)