A cyclist turns around a curve at \(15\ \text{miles/hour}\). If he turns at double the speed, the tendency to overturn is:

1. Doubled
2. Quadrupled
3. Halved
4. Unchanged

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be:
1. \(mg+\dfrac{mv^2}{r}\)
2. \(mg-\dfrac{mv^2}{r}\)
3. \(\dfrac{mv^2g}{r}\)
4. \(\dfrac{v^2g}{r}\)

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 motorcyclist moving with a velocity of \(72\ \text{km/h}\) on a flat road takes a turn on the road at a point where the radius of curvature of the road is \(20\ \text{m}\). The acceleration due to gravity is \(10\ \text{m/s}^2\). To avoid skidding, he must not bend with respect to the vertical plane by an angle greater than:

1. \(𝜃=\tan^{−1}6\)

2. \(𝜃=\tan^{−1}2\)$\mathrm{}$

3. \(𝜃=\tan^{−1}25.92\)$$

4. \(𝜃=\tan^{−1}4\)$$

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 \(r^2\)

2. Independent of \(r\)

3. Proportional to \(r\)

4. Proportional to \(\dfrac 1r\)

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. \(\dfrac{Ml}{M+m}\)

2. \(\dfrac{ml}{M+m}\)

3. \(\dfrac{M+m}{M}l\)

4. \(\dfrac{M+m}{m}l\)

A \(500\ \text{kg}\) car takes a round turn of radius \(50\ \text{m}\) with a velocity of \(36\ \text{km/h}\). The centripetal force is:

1. \(250\ \text{N}\)

2. \(750\ \text{N}\)

3. \(1000\ \text{N}\)

4. \(1200\ \text{N}\)

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

1. \(14\ \text{m/s}\)

2. \(3\ \text{m/s}\)

3. \(3.92\ \text{m/s}\)

4. \(5\ \text{m/s}\)

A body of mass \(5\ \text{kg}\) is moving in a circle of radius \(1\ \text{m}\) with an angular velocity of \(2\ \text{rad/s}\). The centripetal force is:

1. \(10\ \text{N}\)

2. \(20\ \text{N}\)

3. \(30\ \text{N}\)

4. \(40\ \text{N}\)

A stone of mass \(16\ \text{kg}\) is attached to a string \(144\ \text{m}\) 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. \(20\ \text{ms}^{–1}\)
2. \(16\ \text{ms}^{–1}\)
3. \(14\ \text{ms}^{–1}\)
4. \(12\ \text{ms}^{–1}\)