Q. No.A string of length \(L\) is fixed at one end and carries a mass of \(M\) at the other end. The mass makes \((3/\pi) \) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is _____ \(ML.\)
1. \(36\)
2. \(6\)
3. \(18\)
4. \(9\)
1. \(36\)
2. \(6\)
3. \(18\)
4. \(9\)
Subtopic: Â Uniform Circular Motion |
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A block of mass \(2 ~\text{kg}\) is placed on a horizontal disc that rotates with a constant angular velocity of \(4 ~\text{rad/s}.\) The block is located at a distance of \(1~\text{m}\) from the axis of rotation. If the block does not slip relative to the disc, what is the frictional force acting on the block?
1. \(32~\text N\)
2. \(36~\text N\)
3. \(40~\text N\)
4. \(50~\text N\)
Subtopic: Â Uniform Circular Motion |
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A block of mass \(m\) is connected to one end of a spring and kept on a smooth surface. The other end of the spring is connected to fixed shaft rotating with constant angular speed \(\omega .\) Find tension in spring.
1. \(\dfrac{m\omega^2 r}{2}\)
2. \(2m\omega^{2}r\)
3. \(m\omega^{2}r\)
4. \(\dfrac{3}{2}m\omega^{2}r\)
1. \(\dfrac{m\omega^2 r}{2}\)
2. \(2m\omega^{2}r\)
3. \(m\omega^{2}r\)
4. \(\dfrac{3}{2}m\omega^{2}r\)
Subtopic: Â Uniform Circular Motion |
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A car moving with a constant speed of \(2\) m/s in a circle having a radius \(R\). A pendulum is suspended from the ceiling of the car. The angle made by the pendulum with vertical is:
( Take \(R=\frac{8}{15}\) m and \(g=10\) m/s2.)
1. \(30^{\circ}\)
2. \(53^{\circ}\)
3. \(37^{\circ}\)
4. \(60^{\circ}\)
( Take \(R=\frac{8}{15}\) m and \(g=10\) m/s2.)
1. \(30^{\circ}\)
2. \(53^{\circ}\)
3. \(37^{\circ}\)
4. \(60^{\circ}\)
Subtopic: Â Uniform Circular Motion |
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A particle is kept at rest at \(1 ~\text {cm}\) from axis on the disc rotating with angular velocity \(\omega\). If angular velocity is reduced to half of its initial value, then find the distance from axis, where particle again remains at rest
1. \(4 ~\text {cm}\)
2. \(6 ~\text {cm}\)
3. \(8 ~\text {cm}\)
4. \(12 ~\text {cm}\)
1. \(4 ~\text {cm}\)
2. \(6 ~\text {cm}\)
3. \(8 ~\text {cm}\)
4. \(12 ~\text {cm}\)
Subtopic: Â Uniform Circular Motion |
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One end of a massless spring of spring constant k and natural length \(l_0\) is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through a fixed end, then the elongation of the spring will be:
1. \(\frac{\mathrm{k}-\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2} \)
2. \( \frac{\mathrm{m} \omega^2 l_0}{\mathrm{k}+\mathrm{m} \omega^2} \)
3. \( \frac{m \omega^2 l_0}{k-m \omega^2} \)
4. \(\frac{\mathrm{k}+\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2}\)
1. \(\frac{\mathrm{k}-\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2} \)
2. \( \frac{\mathrm{m} \omega^2 l_0}{\mathrm{k}+\mathrm{m} \omega^2} \)
3. \( \frac{m \omega^2 l_0}{k-m \omega^2} \)
4. \(\frac{\mathrm{k}+\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2}\)
Subtopic: Â Uniform Circular Motion |
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A ball is released from rest from point \(P\) of a smooth semi-spherical vessel as shown in the figure. The ratio of the centripetal force and the normal reaction on the ball at point \(Q\) is \(A\) while the angular position of point \(Q\) is \(\alpha\) with respect to point \(P\). Which of the following graphs represents the correct relation between \(A\) and \(\alpha\) when the ball goes from point \(Q\) to point \(R?\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Uniform Circular Motion |
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A disc with a flat small bottom beaker placed on it at a distance \(R\) from its centre is revolving about an axis passing through the centre and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if:
1. \({R} \leq \frac{\mu{g}}{2 \omega^2} \)
2. \(R \leq \frac{\mu g}{\omega^2} \)
3. \(R \geq \frac{\mu g}{2 \omega^2} \)
4. \(R \geq \frac{\mu g}{\omega^2}\)
1. \({R} \leq \frac{\mu{g}}{2 \omega^2} \)
2. \(R \leq \frac{\mu g}{\omega^2} \)
3. \(R \geq \frac{\mu g}{2 \omega^2} \)
4. \(R \geq \frac{\mu g}{\omega^2}\)
Subtopic: Â Uniform Circular Motion |
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A stone of mass m, tied to a string, is being whirled in a vertical circle with a uniform speed. The tension in the string is:
| 1. | the same throughout the motion |
| 2. | minimum at the highest position of the circular path |
| 3. | minimum at the lowest position of the circular path |
| 4. | minimum when the rope is in the horizontal position |
Subtopic: Â Uniform Circular Motion |
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A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is \({K \over \pi}~rev./min\). The value of K is: (Assume the string is massless and unstretchable)
1. 400
2. 300
3. 600
4. 800
1. 400
2. 300
3. 600
4. 800
Subtopic: Â Uniform Circular Motion |
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