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A thin uniform rod of mass 5kg and length 1 m is held in horizontal position with the help of strings attached to ends of rod, other ends of strings are held by some external agent. Now end A is pulled down with speed $V_{A} = 3 t$ and B is pulled down with speed $V_{B} = t$ , where ‘t’ is time in sec. Choose the correct choice(s) at time $t = 0 [T a k e g = 10 m / s^{2}]$

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Angular acceleration of rod is $2 r a d / s^{2}$

Angular acceleration of one end of rod wrt the other end is $2 r a d / s^{2}$

Instantaneous axis of rotation is at a distance of 0.5m from right end of rod

Instantaneous axis of rotation is at a distance of 0.75m from right end of rod

answer is A, B, C.

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Detailed Solution

$a_{C} + L α / 2 = a_{1}; a_{C} - L α / 2 = a_{2}$

$α = \frac{a_{1} - a_{2}}{L} = 2 r a d / s^{2}$

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