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Q. No.A block \(A\) is pushed on a smooth horizontal plane by applying a horizontal force \(F ,\) which causes an acceleration of \({\dfrac g 4}\) (\(g\): acceleration due to gravity). The block does not topple, even though the force acts at its highest point. The normal reaction shifts forward by:
1.
\({\dfrac b 2}\)
2.
\({ \dfrac b 4}\)
3.
\({\dfrac b 8}\)
4.
\(\dfrac b 3\)
Subtopic: Â Torque |
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The centre-of-mass of a uniform solid hemisphere of radius \(R\) is located at a distance of \(\dfrac{3R}{8}\) from its centre \(O.\) If the hemisphere is now cut symmetrically into two identical parts by a single plane, the centre-of-mass of one of the parts is located at a distance from \(O\) of:
1. \(\dfrac{3R}{8}\)
2. \(\dfrac{3R}{4}\)
3. \(\dfrac{3R}{8}\sqrt2\)
4. \(\dfrac{3R}{5}\sqrt2\)
1. \(\dfrac{3R}{8}\)
2. \(\dfrac{3R}{4}\)
3. \(\dfrac{3R}{8}\sqrt2\)
4. \(\dfrac{3R}{5}\sqrt2\)
Subtopic: Â Center of Mass |
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A block of mass \(m\) slides down the smooth inclined surface of a wedge of mass \(M;\) which is itself on a smooth horizontal surface. The centre-of-mass of the system:
| 1. | is stationary |
| 2. | accelerates to the left |
| 3. | accelerates to the right |
| 4. | accelerates downward |
Subtopic: Â Center of Mass |
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A uniform ladder of mass \(10\) kg is placed at an angle against a frictionless vertical wall, as shown in the figure, by applying a horizontal force \(F\) at the bottom \((B)\) of the ladder, towards the wall. (Take \(g=10\) m/s2).
Assume that the ground is frictionless. The force \(F\) equals:
Assume that the ground is frictionless. The force \(F\) equals:
| 1. | \(100\sqrt3\) N | 2. | \(50\sqrt3\) N |
| 3. | \(\dfrac{100}{\sqrt3}\) N | 4. | \(\dfrac{50}{\sqrt3}\) N |
Subtopic: Â Torque |
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Given below are two statements:
| Statement I: | The centre-of-mass of a system of particles lying on a straight line must lie between the two extreme particles. |
| Statement II: | The centre-of-mass of a system of bodies moving with different velocities, cannot be moving with constant velocity. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Â Center of Mass |
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A force is applied to a hollow spherical shell so that it acts through its centre. It causes an acceleration of \(3\) m/s2. If the same force is applied to the spherical shell, acting tangent to its surface, the acceleration will be: (Assuming no friction is available.)
1. \(3\) m/s2
2. \(2\) m/s2
3. zero
4. \(1\) m/s2
1. \(3\) m/s2
2. \(2\) m/s2
3. zero
4. \(1\) m/s2
Subtopic: Â Rotational Motion: Dynamics |
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A uniform chain \(ABC\) is at rest with half of it hanging off the edge of a rough horizontal table. If the total length of the chain is \(2~\text m,\) the centre-of-mass of the chain is located:
| 1. | \(0.25~\text{m}\) below the table | 2. | \(0.5~\text{m}\) below the table |
| 3. | \(0.33~\text{m}\) below the table | 4. | \(0.4~\text{m}\) below the table |
Subtopic: Â Center of Mass |
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The moment of inertia of a uniform right-angled triangular lamina (mass: \(m\)) \(\Delta ABC \) about an axis passing through \(C,\) perpendicular to its plane is:
| 1. | \(m\left(\dfrac{a^2 +b^2}{3}\right ) \) | 2. | \(m\left(\dfrac{a^2 +b^2}{6}\right) \) |
| 3. | \(m\left(\dfrac{a^2 +b^2}{12}\right) \) | 4. | \(m\left(\dfrac{a^2 +b^2}{2}\right) \) |
Subtopic: Â Moment of Inertia |
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The centre-of-mass of a uniform solid cone is located at a distance of \(\dfrac{3}{4} H\) from the vertex of the cone, where \(H\) is its height. The centre-of-mass of a regular solid tetrahedron of height \(H\) is located at a distance of:
1. \(\dfrac{1}{2} H\) from its vertex
2. \(\dfrac{2}{3}H\) from its vertex
3. \(\dfrac{3}{4}H\) from its vertex
4. \(\dfrac{3}{8}H\) from its vertex
1. \(\dfrac{1}{2} H\) from its vertex
2. \(\dfrac{2}{3}H\) from its vertex
3. \(\dfrac{3}{4}H\) from its vertex
4. \(\dfrac{3}{8}H\) from its vertex
Subtopic: Â Center of Mass |
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A uniform rod of length \(L\) is standing upright, pivoted at its lower end. The rod can freely rotate about the pivot. If it is slightly disturbed so that it falls to the ground, the speed of the highest point, when it strikes the ground will be:
| 1. | \(\sqrt{2gL}\) | 2. | \(\sqrt{3gL}\) |
| 3. | \(\sqrt{6gL}\) | 4. | \(\sqrt{gL}\) |
Subtopic: Â Rotational Motion: Dynamics |
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