A block of mass m at the end of a string is whirled round in a vertical circle of radius R. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is 

(1) Rg

(2) (Rg)²

(3) R/g

(4) $\sqrt{Rg}$

A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take g = 10 m/s²) 

(1) 4 m/sec

(2) 6.25 m/sec

(3) 16 m/sec

(4) None of the above

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at (g = 10 m/sec²) 

1. Top of the circle

2. Bottom of the circle

3. Half way down

4. None of the above

The tension in the string revolving in a vertical circle with a mass m at the end which is at the lowest position 

(1) $\frac{m{v}^2}{r}$

(2) $\frac{m{v}^2}{r}-mg$

(3) $\frac{m{v}^2}{r}+mg$

(4) mg

A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is 

(1) 27 cm

(2) 9 cm

(3) 3 cm

(4) 1 cm

A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle is 2 m, then tension in the string when the body is at the top of the circle, is 

(1) 41.56 N

(2) 89.86 N

(3) 109.86 N

(4) 122.4 N

A bucket full of water is revolved in vertical circle of radius 2m. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket ?

(1) 1 sec

(2) 2 sec

(3) 3 sec

(4) 4 sec

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is 

1. $\frac{ML{\omega }^2}{2}$

2. $ML{\omega }^2$

3. $\frac{ML{\omega }^2}{4}$

4. $\frac{M{L}^2{\omega }^2}{2}$

A car is moving in a circular horizontal track of radius \(10~\text{m}\) with a constant speed of \(10~\text{m/s}\). A plumb bob is suspended from the roof of the car by a light rigid rod of length \(1.00~\text{m}\). The angle formed by the rod with respect to the vertical is:

A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration $\alpha$. If the coefficient of friction between the rod and the bead is μ, and gravity is neglected, then the time after which the bead starts slipping is

(1) $\sqrt{\frac{\mu }{\alpha }}$

(2) $\frac{\mu }{\sqrt{\alpha }}$

(3) $\frac{1}{\sqrt{\mu \alpha }}$

(4) Infinitesimal