Two masses M and m are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance 'x' of M from the axis is- 

1. $\frac{Ml}{M+m}$

2. $\frac{ml}{M+m}$

3. $\frac{M+m}{M}l$

4. $\frac{M+m}{m}l$

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is 

1. 250 N

2. 750 N

3. 1000 N

4. 1200 N

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved 

1. 14 m/s

2. 3 m/s

3. 3.92 m/s

4. 5 m/s

A body of mass 5 kg is moving in a circle of radius 1m with an angular velocity of 2 radian/sec. The centripetal force is 

1. 10 N

2. 20 N

3. 30 N

4. 40 N

A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it will be-

1. 20 ms^–1

2. 16 ms^–1

3. 14 ms^–1

4. 12 ms^–1

Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2 

1. 0.14 m/s

2. 140 m/s

3. 1.4 km/s

4. 14 m/s

A ball of mass \(0.1~\text{kg}\) is whirled in a horizontal circle of radius \(1\) m by means of a string at an initial speed of \(10~\text{rpm}\) . Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:

A cyclist riding the bicycle at a speed of $14\sqrt{3}$ms^–1 takes a turn around a circular road of radius $20\sqrt{3}$m without skidding. Given g = 9.8 ms^–2, what is his inclination to the vertical?

1. 30^o

2. 90^o

3. 45^o

4. 60^o

A point mass \(m\) is suspended from a light thread of length \(l,\) fixed at \(O\), and is whirled in a horizontal circle at a constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:

1.		2.
3.		4.

If a cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then coefficient of friction between the cycle tyres and road is 

1. 0.41

2. 0.51

3. 0.61

4. 0.71