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Q. No.For the given system (see figure), the moment of inertia about the diagonal is:
1. \(1 ~\text{kg-m}^2 \)
2. \(2 ~\text{kg-m}^2 \)
3. \(4 ~\text{kg-m}^2 \)
4. \(6~\text{kg-m}^2 \)
Subtopic: Moment of Inertia |
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A uniform disk of mass \(50 ~\text{kg}\) is rolling with the speed of \(0.4 ~\text{m/s}.\) The minimum energy (in J) required to bring the disk to rest is:
1. \(6~\text J\)
2. \(8~\text J\)
3. \(4~\text J\)
4. \(12~\text J\)
1. \(6~\text J\)
2. \(8~\text J\)
3. \(4~\text J\)
4. \(12~\text J\)
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A particle of mass \(m\) is projected with speed \(v\) at an angle of \(30^\circ\) with the horizontal. When the particle is at the maximum height, its angular momentum about the point of projection is:
| 1. | \(\dfrac{mv^3}{16g}\) | 2. | \(\dfrac{\sqrt3 mv^3}{16g}\) |
| 3. | \(\dfrac{mv^3}{3g}\) | 4. | \(\dfrac{\sqrt3mv^3}{8g}\) |
Subtopic: Angular Momentum |
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A uniform disc of mass \(5 ~\text{kg}\) and radius \(2 ~\text m\) is rotating with \(10 ~\text{rad/s}.\) Now another identical disc is gently placed on the first disc. Because of friction, both discs acquire common angular velocity. Then the loss of kinetic energy in process is:
1. \(200~\text J\)
2. \(250~\text J\)
3. \(180~\text J\)
4. \(150~\text J\)
1. \(200~\text J\)
2. \(250~\text J\)
3. \(180~\text J\)
4. \(150~\text J\)
Subtopic: Moment of Inertia |
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A solid cylinder is placed gently over an inclined plane of inclination \(60^\circ.\) The acceleration of the cylinder, when it starts rolling without slipping, is \(\dfrac{g}{\sqrt{x}}\), where \(\mu\) is coefficient of friction. \(\left(\text{Take } g=10~\text{m/s}^2\right)\)
1. \(3\)
2. \(2\)
3. \(5\)
4. \(7\)
1. \(3\)
2. \(2\)
3. \(5\)
4. \(7\)
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A man holding a rod of mass \(m\) as shown in the figure. Find the weight of the rod experienced by him.
1. \(mg\over 2\)
2. \({mg}\over 4\)
3. \(3{mg}\over 2\)
4. \({mg}\over 3\)
1. \(mg\over 2\)
2. \({mg}\over 4\)
3. \(3{mg}\over 2\)
4. \({mg}\over 3\)
Subtopic: Torque |
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A uniform ring and uniform solid sphere roll down the same inclined plane at the same distance. If the ratio of their translational kinetic energies is \(7\over{x}\) then \({x}\) is: (Given mass and radius of the ring and sphere are equal)
1. \(10\)
2. \(15\)
3. \(20\)
4. \(35\)
1. \(10\)
2. \(15\)
3. \(20\)
4. \(35\)
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A body of mass \(1000 ~\text{kg}\) is moving horizontally with a velocity \(6 ~\text{m/s}.\) Another body of mass \(200 ~\text{kg}\) is added gently. Then what will be its new velocity?
1. \(5 ~\text{m/s}\)
2. \(4 ~\text{m/s}\)
3. \(2 ~\text{m/s}\)
4. \(3 ~\text{m/s}\)
1. \(5 ~\text{m/s}\)
2. \(4 ~\text{m/s}\)
3. \(2 ~\text{m/s}\)
4. \(3 ~\text{m/s}\)
Subtopic: Linear Momentum |
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Two identical solid spheres, each of mass \(2 ~\text{kg}\) and radius, \(75 ~\text{cm},\) touch each other. A vertical axis passes through their point of contact as shown in the figure. The moment of inertia of the system of both spheres about this axis is:
| 1. | \(3.15~\text{kg-m}^2\) | 2. | \( 31.5~\text{kg-m}^2\) |
| 3. | \( 0.9~\text{kg-m}^2\) | 4. | \( 9~\text{kg-m}^2\) |
Subtopic: Moment of Inertia |
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A disk of mass \(M\), and radius \(R\) is rotating about an axis passing through its center and perpendicular to its plane with angular speed \(\omega.\) If another disk of mass \(\frac{M}{2}\) and radius \(R\) is gently placed over it then their common angular velocity after some time is:
1. \(\frac{\omega}{5}\)
2. \(\frac{\omega}{2}\)
3. \(\frac{2 \omega}{3}\)
4. \(\frac{\omega}{4}\)
1. \(\frac{\omega}{5}\)
2. \(\frac{\omega}{2}\)
3. \(\frac{2 \omega}{3}\)
4. \(\frac{\omega}{4}\)
Subtopic: Angular Momentum |
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