A force \(F_1\) acts on a particle so as to accelerate it from rest to a velocity \(v.\) The force \(F_1\) is then replaced by \(F_2\) which decelerates it to rest.
1. \(F_1\) must be equal to \(F_2\)
2. \(F_1\) may be equal to \(F_2\)
3. must be unequal to \(F_2\)
4. none of these

Two objects \(A\) and \(B\) are thrown upward simultaneously with the same speed. The mass of \(A\) is greater than the mass of \(B\). Suppose the air exerts a constant and equal force of resistance on the two bodies.

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 \(t_1\) in reaching the maximum height and \(t_2\) in the return journey to the original point. Then:
1. \(t_1 < t_2\)
2. \(t_1 > t_2 \)
3. \(t_1 = t_2\)
4. the relation between \(t_1\) and \(t_2\) 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 show the displacement of a particle going along the \(x\text-\)axis as a function of time. The force acting on the particle is zero in the region:

Choose the correct option from the given ones: