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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Four particles of masses \( 1\text{ kg} \), \( 2\text{ kg} \), \( 3\text{ kg} \), and \( 4\text{ kg} \) have position vectors \( \mathbf{r}_1 = (\hat{\mathbf{i}} + 2\hat{\mathbf{j}} + 3\hat{\mathbf{k}})\text{ m} \), \( \mathbf{r}_2 = (2\hat{\mathbf{i}} - \hat{\mathbf{j}} + \hat{\mathbf{k}})\text{ m} \), \( \mathbf{r}_3 = (-\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - 2\hat{\mathbf{k}})\text{ m} \), and \( \mathbf{r}_4 = (3\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}})\text{ m} \). The magnitude of the position vector of their centre of mass is:

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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Given below are two statements: Statement I: When a girl sitting on a swivel chair stretches her arms horizontally, her moment of inertia about the axis of rotation increases, leading to a decrease in her angular speed. Statement II: In the absence of external torque, the rotational kinetic energy of the girl-chair system remains strictly conserved during the stretching and folding of arms. In the light of the above statements, choose the most appropriate answer from the options given below:

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