A coin, placed on a rotating turntable, slips when it is placed at a distance of \(9\ \text{cm}\) from the centre. If the angular velocity of the turntable is tripled, it will just slip if its distance from the centre is:

1. \(27\ \text{cm}\)
2. \(9\ \text{cm}\)
3. \(3\ \text{cm}\)
4. \(1\ \text{cm}\)

A car is moving in a circular horizontal track of radius \(10~\text{m}\) with a constant speed of \(10~\text{m/s}\). A plumb bob is suspended from the roof of the car by a light rigid rod of length \(1.00~\text{m}\). The angle formed by the rod with respect to the vertical is:

A mass of \(1\ \text{kg}\) is suspended by a string \(A\). Another string \(C\) is connected to its lower end as shown in the given figure. If a sudden jerk is given to \(C\), then:

1. The portion \(AB\) of the string will break
2. The portion \(BC\) of the string will break
3. None of the strings will break
4. The mass will start rotating

A coin is dropped in a lift. It takes time \(t_1\) to reach the floor when the lift is stationary. It takes time \(t_2\) when the lift is moving up with constant acceleration. Then:
1. \(t_1 > t_2\)
2. \(t_1 < t_2\)
3. \(t_1 = t_2\)
4. \(t_1 >> t_2\)

If the tension in the cable of \(1000~\text{kg}\) elevator is \(1000~\text{kg}\) weight, the elevator:

1. is accelerating upwards.

2. is accelerating downwards.

3. may be at rest or accelerating.

4. may be at rest or in uniform motion.

In the given diagram, the acceleration of the car will be:

1. \(0.25\ \text{m/s}^2\)
2. \(2.5\ \text{m/s}^2\)
3. \(5.0\ \text{m/s}^2\)
4. \(0.025\ \text{m/s}^2\)

A particle of mass \(0.3\ \text{kg}\) is subjected to a force \(F = –kx\) with \(k = 15\ \text{N/m}\). What will be its initial acceleration if it is released from a point \(20\ \text{cm}\) away from the origin:
1. \(5\ \text{m/s}^2\)
2. \(10\ \text{m/s}^2\)
3. \(3\ \text{m/s}^2\)
4. \(15\ \text{m/s}^2\)

It is easier to draw up a wooden block along an smooth inclined plane than to haul it vertically, principally because 

(1) The friction is reduced

(2) The mass becomes smaller

(3) Only a part of the weight has to be overcome

(4) ‘g’ becomes smaller

Three identical particles are joined together by a thread as shown in the given figure. All three particles are moving in horizontal circles centred at \(O\). If the velocity of the outermost particle is \(v_0\), then the ratio of tensions in the three sections of the string is:

1. \(3 : 5 : 7\)
2. \(3 : 4 : 5\)
3. \(7 : 11 : 6\)
4. \(3 : 5 : 6\)