A dumbbell consists of two particles of equal mass m (connected with massless rod) separated by a distance 2a. It is initially rigidly attached along a radial line to a disk that is rotating at angular velocity $ω$ rad/s about a fixed vertical axis (see figure). The center of the dumbbell is at a distance R from the center of the disk. Choose the CORRECT statement(s) about the motion of dumbbell after it is suddenly free from disk . Assume no friction between dumbbell and disk and all the motion occurs on a horizontal frictionless plane.

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Kinetic energy of dumbbell will be given by $m a^{2} ω^{2}$ .

Motion of dumbbell will be pure translational.

Angular velocity of dumbbell remains same i.e. $ω$ .

Kinetic energy of dumbbell will be given by $\frac{1}{2} m R^{2} ω^{2}$ .

answer is B.

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Detailed Solution

$KE= \frac{1}{2} {mυ}_{c}^{2} + \frac{1}{2} I_{c} ω^{2}$

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