A car sometimes overturns while taking a turn. When it overturns, it is:

(1) the inner wheel which leaves the ground first.

(2) the outer wheel which leaves the ground first.

(3) both the wheels leave the ground simultaneously.

(4) either wheel leaves the ground first.

A motor cyclist moving with a velocity of 72 km/hour on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 meters. The acceleration due to gravity is 10 m/sec². In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than 

(1) $\theta ={\tan }^{-1}6$

(2) $\theta ={\tan }^{-1}2$

(3) $\theta ={\tan }^{-1}25.92$

(4) $\theta ={\tan }^{-1}4$

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance ‘r’. The speed of the particle is 

(1) Proportional to r²

(2) Independent of r

(3) Proportional to r

(4) Proportional to 1/r

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: