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Q. No.Two particles \(A\) and \(B\) initially at rest, move toward each other under the mutual force of attraction. At an instance when the speed of \(A\) is \(v\) and speed of \(B\) is \(3v,\) the speed of the centre-of-mass will be:
1. \(2v\)
2. zero
3. \(v\)
4. \(4v\)
1. \(2v\)
2. zero
3. \(v\)
4. \(4v\)
Subtopic: Â Center of Mass |
 71%
Level 2: 60%+
NEET - 2023
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Two objects of mass \(10~ \text {kg}\) and \(20~ \text{kg}\) respectively are connected to the two ends of a rigid rod of length \(10~ \text m\) with negligible mass. The distance of the center of mass of the system from the \(10 ~ \text{kg}\) mass is:
| 1. | \(5~ \text m\) | 2. | \(\dfrac{10}{3} \mathrm{~m}\) |
| 3. | \(\dfrac{20}{3} \mathrm{~m}\) | 4. | \(10~ \text m\) |
Subtopic: Â Center of Mass |
 76%
Level 2: 60%+
NEET - 2022
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Three identical spheres, each of mass \(M\), are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to \(2~\text{m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass.
| 1. | \(2(\hat{i}+\hat{j})\) | 2. | \(\hat{i}+\hat{j}\) |
| 3. | \(\frac{2}{3}(\hat{i}+\hat{j})\) | 4. | \(\frac{4}{3}(\hat{i}+\hat{j})\) |
Subtopic: Â Center of Mass |
 68%
Level 2: 60%+
NEET - 2020
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Which of the following statements are correct?
| (a) | centre of mass of a body always coincides with the centre of gravity of the body . |
| (b) | centre of gravity of a body is the point about which the total gravitational torque on the body is zero. |
| (c) | a couple on a body produce both translational and rotation motion in a body. |
| (d) | mechanical advantage greater than one means that small effort can be used to lift a large load. |
| 1. | (a) and (b) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (b) and (d) |
Subtopic: Â Center of Mass |
 62%
Level 2: 60%+
NEET - 2017
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Two persons of masses \(55~\text{kg}\) and \(65~\text{kg}\) respectively, are at the opposite ends of a boat. The length of the boat is \(3.0~\text{m}\) and weighs \(100~\text{kg}.\) The \(55~\text{kg}\) man walks up to the \(65~\text{kg}\) man and sits with him. If the boat is in still water, the centre of mass of the system shifts by:
1. \(3.0~\text{m}\)
2. \(2.3~\text{m}\)
3. zero
4. \(0.75~\text{m}\)
Subtopic: Â Center of Mass |
 77%
Level 2: 60%+
AIPMT - 2012
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Let \(\omega_{1},\omega_{2}\) and \(\omega_{3}\) be the angular speeds of the second hand, minute hand, and hour hand of a smoothly running analog clock, respectively. If \(x_{1},x_{2}\) and \(x_{3}\) are their respective angular distance in \(1~\text{minute},\) then the factor that remains constant \((k)\) is:
| 1. | \(\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}={k}\) |
| 2. | \(\omega_{1}x_{1}=\omega_{2}x_{2}=\omega_{3}x_{3}={k}\) |
| 3. | \(\omega_{1}x_{1}^{2}=\omega_{2}x_{2}^{2}=\omega_{3}x_{3}^{2}={k}\) |
| 4. | \(\omega_{1}^{2}x_{1}=\omega_{2}^{2}x_{2}=\omega_{3}^{2}x_{3}={k}\) |
Subtopic: Â Rotational Motion: Kinematics |
 56%
Level 3: 35%-60%
NEET - 2024
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The angular acceleration of a body moving along the circumference of a circle is:
| 1. | along the axis of rotation |
| 2. | along the radius, away from the centre |
| 3. | along the radius towards the centre |
| 4. | along the tangent to its position |
Subtopic: Â Rotational Motion: Kinematics |
 52%
Level 3: 35%-60%
NEET - 2023
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A particle starting from rest moves in a circle of radius \(r\). It attains a velocity of \(v_0~\text{m/s}\) on completion of \(n\) rounds. Its angular acceleration will be:
| 1. | \( \dfrac{v_0}{n} ~\text{rad} / \text{s}^2\) | 2. | \( \dfrac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \) |
| 3. | \( \dfrac{v_0^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \) | 4. | \( \dfrac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \) |
Subtopic: Â Rotational Motion: Kinematics |
 55%
Level 3: 35%-60%
NEET - 2019
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A sphere of radius \(R\) is cut from a larger solid sphere of radius \(2R\) as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the \(Y\)-axis is:
| 1. | \(\dfrac{7}{57}\) | 2. | \(\dfrac{7}{64}\) |
| 3. | \(\dfrac{7}{8}\) | 4. | \(\dfrac{7}{40}\) |
Subtopic: Â Moment of Inertia |
Level 3: 35%-60%
NEET - 2025
Please attempt this question first.
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Please attempt this question first.
The radius of gyration of a solid sphere of mass \(5~\text{kg}\) about \(XY \text- \text{axis}\) is \(5~\text m\) as shown in the figure. If the radius of the sphere is \(\frac{5x}{\sqrt{7}}~\text m,\) then the value of \(x\) is:
| 1. | \(5\) | 2. | \(\sqrt{2}\) |
| 3. | \(\sqrt{3}\) | 4. | \(\sqrt{5}\) |
Subtopic: Â Moment of Inertia |
 73%
Level 2: 60%+
NEET - 2024
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