A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth’s surface. A block B placed at the top of the wedge takes a time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will

1. take a time longer than T to slide down the wedge

2. take a time shorter than T to slide down the wedge

3. remain at the top of the wedge

4. jump off the wedge

In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle’s motion. A particle of mass m projected upward takes a time t₁ in reaching the maximum height and t₂ in the return journey to the original point. Then

1. t₁ < t₂

2. t₁ > t₂ 

3. t₁ = t₂

4. the relation between t₁ and t₂ depends on the mass of the particle

A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator in a time \(t_1\) if the elevator is stationary and in time \(t_2\) if it is moving uniformly. Then:

A free ²³⁸U nucleus kept in a train emits an alpha particle. When the train is stationary, a nucleus decays and a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x at time t after the decay. If the decay takes place while the train is moving at a uniform velocity v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay as measured by the passenger is

1. x + v t

2. x – v t

3. x

4. depends on the direction of the train

A reference frame attached to the earth

(a) is an inertial frame by definition

(b) cannot be an inertial frame because the earth is revolving around the sun

(c) is an inertial frame because Newton’s laws are applicable in this frame

(d) cannot be an inertial frame because the earth is rotating about its axis

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (a) and (d)

4. (b) and (d)

A particle stays at rest as seen in a frame. We can conclude that

(a) the frame is inertial

(b) resultant force on the particle is zero

(c) the frame may be inertial but the resultant force on the particle is zero

(d) the frame may be non-inertial but there is a nonzero resultant force

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

A particle is found to be at rest when seen from a frame S₁ and moving with a constant velocity when seen from another frame S₂. Mark out the possible options.

(a) Both the frames are inertial

(b) Both the frames are non-inertial

(c) S₁ is inertial and S₂ is non-inertial

(d) S₁ is non-inertial and S₂ is inertial

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (a)

4. (a) and (d)

The figures shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region

(a) AB

(b) BC

(c) CD

(d) DE

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (a) and (c)

4. (c) and (d)

The figure shows a heavy block kept on a frictionless surface and being pulled by two ropes of equal mass m. At t = 0, the force on the left rope is withdrawn but the force on the right end continues to act. Let F₁ and F₂ be the magnitudes of the forces by the right rope and the left rope on the block respectively.

1. F₁ = F₂ = F for t < 0

2. F₁ = F₂ = F + mg for t < 0

3. F₁ = F, F₂ = F for t > 0

4. F₁ < F,  F₂ = F for t > 0

The force exerted by the floor of an elevator on the foot of a person standing there is more than the weight of the person if the elevator is

(a) going up and slowing down

(b) going up and speeding up

(c) going down and slowing down

(d) going down and speeding up

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these