A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force F₁ and B presses the track with a force F₂.

1. F₁ > F₂

2. F₁ < F₂

3. F₁ = F₂

4. the information is insufficient to find the relation between F₁ and F₂

If the earth stops rotating, the apparent value of g on its surface will

1. increase everywhere

2. decrease everywhere

3. remain the same everywhere

4. increase at some places and remain the same at some other places

A rod of length L is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. Let T₁ and T₂ be the tensions at the points L/4 and 3L/4 away from the pivoted ends.

1. T₁ > T₂

2. T₂ > T₁

3. T₁ = T₂

4. The relation between T₁ and T₂ depends on whether the rod rotates clockwise or anticlockwise

A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. The car moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some distance. Let R be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is.

1. mg

2. \(\mathrm{mg}-\frac{\mathrm{mv}^{2}}{\mathrm{R}}\)

3. \(m g+\frac{m v^{2}}{R}\)

4. zero

Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension in the string is mg cosθ.

1. always

2. never

3. at the extreme positions

4. at the mean position

An object follows a curved (circular) path. The following quantities may remain constant during the motion.

Choose the correct option from the options given below:

Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 km/s.

1. The average velocity of the earth from 1st Jan, 90 to 30th June, 90 is zero

2. The average acceleration during the above period is 60 km/s²

3. The average speed from 1st Jan, 90 to 31st Dec, 90 is zero

4. The instantaneous acceleration of the earth points towards the sun

The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. Its

(a) velocity remains constant

(b) speed remains constant

(c) acceleration remains constant

(d) tangential acceleration remains constant

Choose the correct option:

1. (a) and (d)

2. (b) and (d)

3. (c) and (d)

4. (a) and (c)

A particle is going in a spiral path as shown in the figure with constant speed.

A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a.

(a) The acceleration of the car is towards the centre of the path

(b) The magnitude of the frictional force on the car is greater than \(\frac{mv^2}{r}\)

(c) The friction coefficient between the ground and the car is not less than a/g

(d) The friction coefficient between the ground and the car is µ = tan^–1 \(\frac{v^2}{rg}\)

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these