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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 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. \(\dfrac{\sqrt3mv^3}{8g}\)
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 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 particle of mass \(2~\text{kg}\) is on a smooth horizontal table and moves in a circular path of radius \(0.6~\text{m}.\) The height of the table from the ground is \(0.8~\text{m}.\) If the angular speed of the particle is \(12~\text{rad s}^{-1},\) the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
1. \(14.4~\text{kg m}^2\text{s}^{-1}\)
2. \(8.64~\text{kg m}^2\text{s}^{-1}\)
3. \(20.16~\text{kg m}^2\text{s}^{-1}\)
4. \(11.52~\text{kg m}^2\text{s}^{-1}\)
1. \(14.4~\text{kg m}^2\text{s}^{-1}\)
2. \(8.64~\text{kg m}^2\text{s}^{-1}\)
3. \(20.16~\text{kg m}^2\text{s}^{-1}\)
4. \(11.52~\text{kg m}^2\text{s}^{-1}\)
Subtopic: Angular Momentum |
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Consider a thin, uniform square sheet made of a rigid material. If its side is \(a\), mass \(m\) and moment of inertia \({I}\) about one of its diagonals, then:
1. \({I}>\dfrac{{ma}^2}{12}\)
2. \({I}=\dfrac{{ma}^2}{12}\)
3. \(\dfrac{{ma}^2}{24}<{I}<\dfrac{{ma}^2}{12}\)
4. \({I}=\dfrac{{ma}^2}{24}\)
1. \({I}>\dfrac{{ma}^2}{12}\)
2. \({I}=\dfrac{{ma}^2}{12}\)
3. \(\dfrac{{ma}^2}{24}<{I}<\dfrac{{ma}^2}{12}\)
4. \({I}=\dfrac{{ma}^2}{24}\)
Subtopic: Moment of Inertia |
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A uniform thin rod \({AB}\) of length \({L}\) has linear mass density \({\mu(x)=}a+\frac{bx}{L},\) where \({x}\) is measured from \({A}.\) If the centre of mass of the rod lies at a distance of \(\left(7\over 12\right)L\) from \({A},\) then \({a}\) and \({b}\) are related as:
1. \({a=2b}\)
2. \({2a=b}\)
3. \({a=b}\)
4. \({3a=2b}\)
1. \({a=2b}\)
2. \({2a=b}\)
3. \({a=b}\)
4. \({3a=2b}\)
Subtopic: Center of Mass |
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A uniform solid cylindrical roller of mass '\(m\)' is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is '\(a\)' and it is rolling without slipping then the value of '\(F\)' is:
1. \({ma}\)
2. \(2{ma}\)
3. \(\frac{5}{3}{ma}\)
4. \(\frac{3}{2}{ma}\)
1. \({ma}\)
2. \(2{ma}\)
3. \(\frac{5}{3}{ma}\)
4. \(\frac{3}{2}{ma}\)
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