A boy of mass M is applying a horizontal force to slide a box of mass M' on a rough horizontal surface. The coefficient of friction between the shoes of the boy and the floor is µ and that between the box and the floor is µ'. In which of the following cases it is certainly not possible to slide the box?

1. µ < µ’, M < M’

2. µ > µ’, M < M’

3. µ < µ', M'> M’

4. µ > µ', M > M’

Let \(F,F_N\) and \(f\) denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero,

Choose the correct option:

The contact force exerted by a body A on another body B is equal to the normal force between the bodies. We conclude that

(a) the surfaces must be frictionless

(b) the force of friction between the bodies is zero

(c) the magnitude of normal force equals that of friction

(d) the bodies may be rough but they don’t slip on each other

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (b) and (d)

4. (a) and (c)

Mark the correct statements about the friction between two bodies.

Choose the correct option:

A block is placed on a rough floor and a horizontal force \(F\) is applied on it. The force of friction \(f\) by the floor on the block is measured for different values of \(F\) and a graph is plotted between them.

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

Consider a vehicle going on a horizontal road towards the east. Neglect any force by the air. The frictional forces on the vehicle by the road

(a) is towards east if the vehicle is accelerating

(b) is zero if the vehicle is moving with a uniform velocity

(c) must be towards the east

(d) must be towards the west

Choose the correct option:

1. (a) and (b)

2. (a) and (c)

3. (b) and (c)

4. (c) and (d)

When a particle moves in a circle with a uniform speed

1. its velocity and acceleration are both constant

2. its velocity is constant but the acceleration changes

3. its acceleration is constant but the velocity changes

4. its velocity and acceleration both change

Two cars having masses m₁ and m₂ move in circles of radii r₁ and r₂ respectively. If they complete the circles in equal time, the ratio of their angular speeds ω₁ / ω₂ is

1. m₁ / m₂

2. r₁ / r₂

3. m₁r₁ / m₂r₂

4. 1

A car moves at a constant speed on a road as shown in the figure. The normal force by the road on the car is \(N_A\) and \(N_B\) when it is at the points \(A\) and \(B\) respectively.

A particle of mass \(m\) is observed from an inertial frame of reference and is found to move in a circle of radius \(r\) with a uniform speed \(v\). The centrifugal force on it is: