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Q. No.Two blocks are joined by a light spring of spring constant, \(k=1000\) N/m, and are placed at rest on a horizontal frictionless table. A horizontal force of \(6\) N acts on the \(2\) kg block. The acceleration of the centre-of-mass of the system is:
1. \(3\) m/s2
2. \(2\) m/s2
3. \(1.5\) m/s2
4. \(4.5\) m/s2
Subtopic: 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).
The normal reaction of the ground on the ladder is:
1. \(100\) N
2. \(100\sqrt3\) N
3. \(50\) N
5. \(50\sqrt3\) N
The normal reaction of the ground on the ladder is:
1. \(100\) N
2. \(100\sqrt3\) N
3. \(50\) N
5. \(50\sqrt3\) N
Subtopic: Torque |
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The angular speed of a flywheel moving with uniform angular acceleration changes from \(1200\) rpm to \(3120\) rpm in \(16\) s. The angular acceleration in rad/s² is:
1. \(104 \pi\)
2. \(2\pi\)
3. \(4\pi\)
4. \(12\pi\)
1. \(104 \pi\)
2. \(2\pi\)
3. \(4\pi\)
4. \(12\pi\)
Subtopic: Rotational Motion: Kinematics |
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An energy of \(484\) J is spent in increasing the speed of a flywheel from \(60\) rpm to \(360\) rpm. The moment of inertia of the flywheel is:
1. \(0.7\) kg-m2
2. \(3.22\) kg-m2
3. \(30.8\) kg-m2
4. \(0.07\) kg-m2
1. \(0.7\) kg-m2
2. \(3.22\) kg-m2
3. \(30.8\) kg-m2
4. \(0.07\) kg-m2
Subtopic: Moment of Inertia |
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A uniform disc of mass \(m\) and radius \(r\) is rotating freely about its own axis, which is kept vertical. There is a small insect of mass \(\frac m2\) sitting on the periphery of the disc, also rotating with the disc. The initial angular speed of the disc is \(\omega_0.\) The insect moves radially inward and finally reaches the centre. The final angular speed of the disc is:
1. \(\omega_0\)
2. \(2\omega_0\)
3. \(\frac32\omega_0\)
4. \(\frac52\omega_0\)
1. \(\omega_0\)
2. \(2\omega_0\)
3. \(\frac32\omega_0\)
4. \(\frac52\omega_0\)
Subtopic: Angular Momentum |
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A block \(A\) is pushed on a smooth horizontal plane by applying a horizontal force \(F ,\) which causes an acceleration of \({g \over 4}\) (\(g\): 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. \({ b\over 2}\)
2. \({ b\over 4}\)
3. \({ b\over 8}\)
4. \(b\over 3\)
1. \({ b\over 2}\)
2. \({ b\over 4}\)
3. \({ b\over 8}\)
4. \(b\over 3\)
Subtopic: Torque |
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Two particles \(A\) and \(B\) initially at rest, move towards each other under mutual force of attraction. At an instance when the speed of \(A\) is \(v\) and speed of \(B\) is \(3v\), the speed of centre of mass is:
| 1. | \(2v\) | 2. | zero |
| 3. | \(v\) | 4. | \(4v\) |
Subtopic: Center of Mass |
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A uniform rod of mass \(m\) and length \(L\) is struck at both ends by two particles of masses m, each moving with identical speeds \(u,\) but in opposite directions, perpendicular to its length. The particles stick to the rod after colliding with it. The system rotates with an angular speed:
1. \(\frac{u}{L}\)
2. \(\frac{2u}{L}\)
3. \(\frac{12u}{7L}\)
4. \(\frac{6u}{L}\)
Subtopic: Angular Momentum |
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If there is no external force acting on a non-rigid body which of the following quantities must remain constant?
| a. | angular momentum |
| b. | linear momentum |
| c. | kinetic energy |
| d. | moment of inertia |
| 1. | (a) and (b) |
| 2. | (b) and (c) |
| 3. | (c) and (d) |
| 4. | (a) and (d) |
Subtopic: Angular Momentum |
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A body is in pure rotation. The linear speed \(v\) of a particle, the distance \(r\) of the particle from the axis and the angular velocity \(\omega\) of the body are related as \(w=\dfrac{v}{r}\). Thus:
1. \(w\propto\dfrac{1}{r}\)
2. \(w\propto\ r\)
3. \(w=0\)
4. \(w\) is independent of \(r\)
Subtopic: Rotational Motion: Kinematics |
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