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.

(a)	The graph is a straight line of slope \(45^{\circ}.\)
(b)	The graph is a straight line parallel to the \(F\)-axis.
(c)	The graph is a straight line of slope \(45^{\circ}\) for small \(F\) and a straight line parallel to the \(F\)-axis for large \(F.\)
(d)	There is a small kink on the graph.

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:

A particle of mass m rotates with a uniform angular speed ω. It is viewed from a frame rotating about the Z-axis with a uniform angular speed ω₀. The centrifugal force on the particle is

1. \(\mathrm{m} \omega^{2} \mathrm{a}\)

2. \(\mathrm{m} \omega_{0}^{2} \mathrm{a}\)

3. \(\left(\frac{\omega+\omega_{0}}{2}\right)^{2} \mathrm{a}\)

4. \(\mathrm{m} \omega ~\omega_{0} \mathrm{a}\)

A particle is kept fixed on a turntable rotating uniformly. As seen from the ground, the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 cm/s². The particle is now shifted to a new position to make the radius half of the original value. The new values of the speed and acceleration will be :

1. 10 cm/s, 10 cm/s²

2. 10 cm/s, 80 cm/s²

3. 40 cm/s, 10 cm/s²    

4. 40 cm/s, 40 cm/s²

Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We. conclude that in this position

1. \(\mathrm{mg}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}\)

2. mg is greater than \(\frac{\mathrm{mv}^{2}}{\mathrm{r}}\)

3. mg is not greater than \(\frac{\mathrm{mv}^{2}}{\mathrm{r}}\)

4. mg is not less than \(\frac{\mathrm{mv}^{2}}{\mathrm{r}}\)

A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move

1. towards the centre    

2. away from the centre

3. along a tangent

4. will stop