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 

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 particle of mass 0.3 kg is subjected to a force F = –kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin

(1) 5 m/s²

(2) 10 m/s²

(3) 3 m/s²

(4) 15 m/s²

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

1. 0.25 m/sec²

2. 2.5 m/sec²

3. 5.0 m/sec²

4. 0.025 m/sec²

If the tension in the cable of 1000 kg elevator is 1000 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 t₁ to reach the floor when lift is stationary. It takes time t₂ when the lift is moving up with constant acceleration. Then:

(1) t₁ > t₂

(2) t₂ > t₁

(3) t₁ = t₂

(4) t₁ >> t₂

A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see 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 turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is 

(1) 27 cm

(2) 9 cm

(3) 3 cm

(4) 1 cm

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in horizontal circles centred at O. If the velocity of the outermost particle is v₀, 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