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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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Two particles each of mass \(2~\text{kg}\) are placed as shown in the \(xy\) plane. If the distance of the centre of mass from the origin is \(\dfrac{4\sqrt 2}{x},\) then the value \(x\) is:
1. \(2\)
2. \(5 \)
3. \(6 \)
4. \(8\)
1. \(2\)
2. \(5 \)
3. \(6 \)
4. \(8\)
Subtopic: Center of Mass |
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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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A body of mass \(m\) is projected with speed \(u\) at an angle \(45^\circ\) with the horizontal. The angular momentum of the body, about the point of projection, when the body is at its highest point, is:
1. \( \dfrac{\sqrt2m u^3}{8g}\)
2. \( \dfrac{\sqrt2m u^3}{9g}\)
3. \( \dfrac{\sqrt2m u^3}{6g}\)
4. \( \dfrac{\sqrt2m u^3}{4g}\)
1. \( \dfrac{\sqrt2m u^3}{8g}\)
2. \( \dfrac{\sqrt2m u^3}{9g}\)
3. \( \dfrac{\sqrt2m u^3}{6g}\)
4. \( \dfrac{\sqrt2m u^3}{4g}\)
Subtopic: Angular Momentum |
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