Q. No.Moment of inertia about an axis \(AB~\) for a rod of mass \(40~\text{kg}\) and length \(3~\text{m}\) is same as that of a solid sphere of mass of \(10~\text{kg}\) and radius \(R\) about an axis parallel to \(AB~\) axis with separation of \(3~\text{m}\) as shown in figure below. The value of \(R\) is given as \(\sqrt{\dfrac{\alpha}{2}}\). The value of \(\alpha\)
1. \(5\)
2. \(10\)
3. \(15\)
4. \(20\)
1. \(5\)
2. \(10\)
3. \(15\)
4. \(20\)
Subtopic: Moment of Inertia |
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A solid sphere of mass \(M\) \(R\) \(M/8\) \(r\) \(t\) \(2R~\) \(I_1\) \(I_2\)
1. \(35\)
2. \(70\)
3. \(140\)
4. \(210\)
1. \(35\)
2. \(70\)
3. \(140\)
4. \(210\)
Subtopic: Moment of Inertia |
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Two identical thin rods of mass \(M~\text{kg}\) and length \(L~\text{m}\) are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point \(P\) and perpendicular to the plane of the rods is \(\dfrac{{x}}{12} {ML}^2 ~\text{kg m}^2\). The value of \(x\) is:
1. \(17\)
2. \(13\)
3. \(19\)
4. \(20\)
1. \(17\)
2. \(13\)
3. \(19\)
4. \(20\)
Subtopic: Moment of Inertia |
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A solid sphere of mass \(5~ \text{kg}\) and radius \(10~\text{cm}\) is kept in contact with another solid sphere of mass \(10~ \text{kg}\) and radius \(20~\text{cm}.\) The moment of inertia of this pair of spheres about the tangent passing through the point of contact is:
1. \(0.36\) kg-m2
2. \(0.72\) kg-m2
3. \(0.18\) kg-m2
4. \(0.63\) kg-m2
1. \(0.36\) kg-m2
2. \(0.72\) kg-m2
3. \(0.18\) kg-m2
4. \(0.63\) kg-m2
Subtopic: Moment of Inertia |
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A circular disc has radius \(R_1\) and thickness \(T_1\). Another circular disc made of the same material has radius \(R_2\) and thickness \(T_2.\) If the moment of inertia of both discs are same and \(\dfrac{R_1}{R_2}=2\) then \(\dfrac{T_1}{T_2}=\dfrac{1}{\alpha}.\) The value of \(\alpha\) is:
1. \(16\)
2. \(10\)
3. \(17\)
4. \(18\)
1. \(16\)
2. \(10\)
3. \(17\)
4. \(18\)
Subtopic: Moment of Inertia |
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The moment of inertia of a square loop made of four uniform solid cylinders each having radius \(R\) and length \(L\) \((R<L)\) about an axis passing through the mid-points of opposite sides, is (Take the mass of the entire loop as \(M\)):
1. \(\dfrac{3}{8} {MR}^2+\dfrac{7}{12} {ML}^2\)
2. \(\dfrac{3}{4} {MR}^2+\dfrac{1}{6} {ML}^2\)
3. \(\dfrac{3}{4}{MR}^2+\dfrac{7}{12} {ML}^2\)
4. \(\dfrac{3}{8} {MR}^2+\dfrac{1}{6} {ML}^2\)
1. \(\dfrac{3}{8} {MR}^2+\dfrac{7}{12} {ML}^2\)
2. \(\dfrac{3}{4} {MR}^2+\dfrac{1}{6} {ML}^2\)
3. \(\dfrac{3}{4}{MR}^2+\dfrac{7}{12} {ML}^2\)
4. \(\dfrac{3}{8} {MR}^2+\dfrac{1}{6} {ML}^2\)
Subtopic: Moment of Inertia |
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Suppose there is a uniform circular disc of mass \(M~\text{kg}\) and radius \(r~\text{m}\) shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis \(A\) of the disc is given by \(\dfrac{{x}}{256} {Mr}^2 .\) The value of \(x\) is:
1. \(190\)
2. \(109\)
3. \(150\)
4. \(200\)
1. \(190\)
2. \(109\)
3. \(150\)
4. \(200\)
Subtopic: Moment of Inertia |
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A uniform solid cylinder of length \( L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1.\) A small co-centric cylinder of length \(L/2\) and radius \(R/3\) carved from this cylinder has moment of inertia about its axis equals to \(I_2.\) The ratio \(\dfrac{I_1}{I_2}\) is:
1. \(162\)
2. \(170\)
3. \(180\)
4. \(190\)
1. \(162\)
2. \(170\)
3. \(180\)
4. \(190\)
Subtopic: Moment of Inertia |
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A solid sphere of radius \(10~\text{cm}\) is rotating about an axis which is at a distance \(15~\text{cm}\) from its centre. The radius of gyration about this axis is \(\sqrt {n}~\text{cm}\). The value of \(n\) is:
1. \(230\)
2. \(210\)
3. \(240\)
4. \(265\)
1. \(230\)
2. \(210\)
3. \(240\)
4. \(265\)
Subtopic: Moment of Inertia |
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A rod of linear mass density \(λ \) and length \(L \) is bent to form a ring of radius \(R.\) Moment of inertia of ring about any of its diameter is:
1. \(\dfrac{\lambda L^3}{16 \pi^2}\)
2. \(\dfrac{\lambda L^3}{12}\)
3. \(\dfrac{\lambda L^3}{4 \pi^2}\)
4. \(\dfrac{\lambda L^3}{8 \pi^2}\)
1. \(\dfrac{\lambda L^3}{16 \pi^2}\)
2. \(\dfrac{\lambda L^3}{12}\)
3. \(\dfrac{\lambda L^3}{4 \pi^2}\)
4. \(\dfrac{\lambda L^3}{8 \pi^2}\)
Subtopic: Moment of Inertia |
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