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

A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of

1. 1 cm

2. 2 cm

3. 4 cm

4. 8 cm

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it

1. increases

2. decreases

3. remains the same

4. fluctuates

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let F_A, F_B and F_C be the normal forces exerted by the cars on the bridges when they are in the middle of bridges.

1. F_A is maximum of the three forces

2. F_B is maximum of the three forces

3. F_C is maximum of the three forces

4. F_A = F_B = F_C

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