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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

हिन्दी

Two particles of masses \( 3\text{ kg} \) and \( 5\text{ kg} \) are separated by a distance of \( 16\text{ m} \). If the \( 3\text{ kg} \) mass is moved towards the centre of mass by \( 4\text{ m} \), what distance must the \( 5\text{ kg} \) mass be moved so that the position of the centre of mass remains unchanged?

  1. \( 2.4\text{ m} \text{ towards CM} \)
  2. \( 3.2\text{ m} \text{ towards CM} \)
  3. \( 2.4\text{ m} \text{ away from CM} \)
  4. \( 1.6\text{ m} \text{ towards CM} \)

Correct answer · Option 1

\( 2.4\text{ m} \text{ towards CM} \)

Explanation

For CM position to remain unchanged: \( m_1 \Delta x_1 + m_2 \Delta x_2 = 0 \implies 3(+4) + 5(\Delta x_2) = 0 \implies \Delta x_2 = -2.4\text{ m} \), which means moving \( 2.4\text{ m} \) towards the CM.

Related questions

Given below are two statements: Statement I: The kinetic energy of a body of moment of inertia \( I \) rotating with an angular velocity \( \omega \) about a fixed axis is given by \( K = \frac{1}{2} I \omega^2 \). Statement II: The moment of inertia of a rotating rigid body changes if its angular velocity is doubled. In the light of the above statements, choose the most appropriate answer from the options given below:→Given two vectors \( \mathbf{a} = 3\hat{i} - 4\hat{j} + 5\hat{k} \) and \( \mathbf{b} = -2\hat{i} + \hat{j} - 3\hat{k} \), the cross product \( \mathbf{a} \times \mathbf{b} \) is equal to:→Consider the following statements regarding rotational motion about a fixed axis: (A) Only those components of external torques that lie along the axis of rotation can cause the body to rotate about the axis. (B) Torques perpendicular to the fixed axis are balanced by the constraint forces exerted by the hinges/supports. (C) Forces parallel to the axis of rotation produce non-zero torque about that axis. (D) The rate of work done by an external torque \( \tau \) rotating a body with angular speed \( \omega \) is given by \( P = \tau \omega \). How many of the above statements are correct?→In an L-shaped uniform lamina formed by three identical squares of side length \( b = 2\text{ m} \) as oriented in Fig. 6.11 (with bottom-left square at origin having vertices from \( (0,0) \) to \( (2,2) \)), the coordinate of the centre of mass is:→
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