If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be

1. $mg+\frac{m{v}^2}{r}$

2. $mg-\frac{m{v}^2}{r}$

3. $\frac{m^2{v}^{2}g}{r}$

4. $\frac{v^{2}g}{r}$

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: