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

A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\mathrm{\theta }$ with the vertical

1. ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the forward direction

2. ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the upward direction 

3. ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the backward direction

4. ${\tan }^{-1}\left(\frac{g}{a}\right)$ in the forward directions 

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. \(15\ \text{m/s}^2\)

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. \(0.025\ \text{m/s}^2\)

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.

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. \(t_1 >> t_2\)

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 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 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. \(1\ \text{cm}\)

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. \(3 : 5 : 6\)