If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be:

(a)	going up with increasing speed
(b)	going down with increasing speed
(c)	going up with uniform speed
(d)	going down with uniform speed

 
Choose the correct option:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. all of the above

A particle is observed from two frames \(S_1\) and \(S_2.\) The frame \(S_2\) moves with respect to \(S_1\) with an acceleration \(a.\) Let \(F_1\) and \(F_2\) be the pseudo forces on the particle when seen from \(S_1\) and \(S_2\) respectively. Which of the following are not possible?
1. \(F_1=0,~F_2\neq0\)
2. \(F_1\neq0,~F_2=0\)
3. \(F_1\neq0,~F_2\neq0\)
4. \(F_1=0,~F_2=0\)

A person reports that a particle has a non-zero acceleration even though no force is acting on it. Which of the following could explain this observation?

In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

1. increase

2. decrease

3. remain the same    

4. may increase or decrease

While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure

1. larger friction

2. smaller friction

3. larger normal force

4. smaller normal force

A body of mass M is kept on a rough horizontal surface (friction coefficient = µ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F where

1. F = Mg

2. F = µ Mg

3. Mg  ≤ F ≤  Mg \(\sqrt{1+\mu^2}\)

4. Mg  ≥ F ≥ Mg \(\sqrt{1-\mu^2}\)

A scooter starting from rest moves with constant acceleration for a time Δt₁ then with a constant velocity for the next Δt₂ and finally with a constant deceleration for the next Δt₃ to come to rest. A 500 N man sitting on the scooter behind the driver manages to stay at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is

1. 500 N throughout the journey

2. less than 500 N throughout the journey

3. more than 500 N throughout the journey

4. > 500 N for time Δt₁ and Δt₃ and 500 N for Δt₂

Consider the situation shown in the figure. The wall is smooth but the surfaces of \(A\) and \(B\) in contact are rough. The friction on \(B\) due to \(A\) in equilibrium:

           
1. is upward
2. is downward
3. is zero
4. the system cannot remain in equilibrium

Suppose all the surfaces in the previous problem are rough. The direction of friction on B due to A

1. is upward

2. is downward

3. is zero

4. depends on the masses of A and B

Previous problem: Consider the situation shown in the figure. The wall is smooth but the surfaces of A and B in contact are rough.

Two cars of unequal masses use similar tyres. If they are moving at the same initial speed, the minimum stopping distance

1. is smaller for the heavier car

2. is smaller for the lighter car

3. is the same for both cars

4. depends on the volume of the car