Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in horizontal circles centred at O. If the velocity of the outermost particle is v₀, then the ratio of tensions in the three sections of the string is 

1. 3 : 5 : 7

2. 3 : 4 : 5

3. 7 : 11 : 6

4. 3 : 5 : 6

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 string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/π revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is 

1. ML

2. 2 ML

3. 4 ML

4. 16 ML

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

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500 m/sec with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is 

1. 550 N

2. 50 N

3. 250 N

4. 250 dyne

A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively 

1. g, g

2. g – a, g – a

3. g – a , g

4. a, g

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be 

1. $mg \cos \theta$

2. $mg \sin \theta$

3. mg

4. $mg/\cos \theta$

A particle moves in the \(XY\text-\)plane under the action of a force \(F\) such that the components of its linear momentum \(p\) at any time \(t\) are \(p_x = 2 \cos t\),  \(p_y = 2 \sin t\). The angle between \(F\) and \(p\) at time \(t\) will be: