The height at which the weight of a body becomes \(\left ( \frac{1}{16} \right )^\mathrm{th}\) of its weight on the surface of the earth (radius \(R\)) is:
1. \(5R\)
2. \(15R\)
3. \(3R\)
4. \(4R\)

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It:

1. will become rigid showing no movement

2. will stay in any position

3. will stay in north-south direction only

4. will stay in east-west direction only

In the circuit shown cells, \(A\) and \(B\) have negligible resistance. For \(V_A =12 ~\text{V},\) \(R_1 = 500 ~\Omega ,\) and $\mathrm{}$\(R = 100 ~\Omega ,\) the galvanometer \((\text{G}) \) shows no deflection. The value of \(V_B\) is: 

Four-point charges \(-Q, -q,~ 2q~\text{and}~2Q \) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the center of the square is zero is:
1. \(Q= -q\)
2. \(Q= -2q\)
3. \(Q= q\)
4. \(Q= 2q\)

A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:

A solid cylinder of mass \(3\) kg is rolling on a horizontal surface with a velocity of \(4\) ms^-1. It collides with a horizontal spring of force constant \(200\) Nm^-1. The maximum compression produced in the spring will be:
1. \(0.5\) m
2. \(0.6\) m
3. \(0.7\) m
4. \(0.2\) m

One mole of an ideal gas goes from an initial state \(A\) to the final state \(B\) with two processes. It first undergoes isothermal expansion from volume \(V\) to \(3V\) and then its volume is reduced from \(3V\) to \(V\) at constant pressure. The correct \((P-V)\) diagram representing the two processes is:

1.		2.
3.		4.