A point mass \(m\) is moved in a vertical circle of radius \(r\) with the help of a string. The velocity of the mass is \(\sqrt{7 g r} \) at the lowest point.
The tension in the string at the lowest point will be:
1. \(6mg\)
2. \(7mg\)
3. \(8mg\)
4. \(mg\)
A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
1. | \(60^{\circ}\) angle from vertical | inclined at a
2. | the mass is at the highest point |
3. | the wire is horizontal |
4. | the mass is at the lowest point. |
A particle of mass \(m\) having speed \(v\) goes in a vertical circular motion such that its centre is at its origin, as shown in the figure. If at any instant the angle made by the string with a negative \(y\text-\)axis is \(\theta\) then the tension in the string is:
[Take radius = \(R\)]
1. \(mg\sin\theta+ \frac{mv^2}{R}\)
2. \(mg\cos\theta- \frac{mv^2}{R}\)
3. \(mg\cos\theta+ \frac{mv^2}{R}\)
4. \(mg\sin\theta- \frac{mv^2}{R}\)
A bucket full of water tied with the help of a \(2\) m long string performs a vertical circular motion. The minimum angular velocity of the bucket at the uppermost point so that water will not fall will be:
1. \(2\sqrt{5}\) rad/s
2. \(\sqrt{5}\) rad/s
3. \(5\) rad/s
4. \(10\) rad/s
The kinetic energy 'K' of a particle moving in a circular path varies with the distance covered S as K = a, where a is constant. The angle between the tangential force and the net force acting on the particle is: (R is the radius of the circular path)
1.
2.
3.
4.
A stone of mass \(\mathrm{m}\) tied to the end of a string revolves in a vertical circle of radius \(\mathrm{R}.\) The magnitude of net forces at the lowest and highest points of the circle directed vertically downwards are:
Lowest point | Highest point | |
1. | \(\mathrm{mg}-\mathrm{T_1}\) | \(\mathrm{mg}+\mathrm{T_2}\) |
2. | \(\mathrm{mg}+\mathrm{T_1}\) | \(\mathrm{mg}+\mathrm{T_2}\) |
3. | ||
4. |
( and denote the tension and speed at the lowest point. and denote corresponding values at the highest point.)
The angle between the position vector and the acceleration vector of a particle in non-uniform circular motion (centre of the circle is taken as the origin) will be:
1. 0°
2. 45°
3. 75°
4. 135°