A puck is moving in a circle of radius r with a constant speed $V_{0}$ on a level frictionless table. A string is attached to the puck which holds it in the circle. The string passes through a frictionless hole and is attached on the other end to a hanging object of mass M. The puck is now made to move with a speed $v = 3 v_{0}$ but still in circle. The mass of the hanging object is left unchanged. The acceleration a of the puck and the radius r of the circle are now given by (a₀ is the initial acceleration of the puck)

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$a^{'} = 9 a_{0} a n d r^{'} = r_{0}$

$a^{'} = a_{0} a n d r^{'} = 9 r_{0}$

$a^{'} = 9 a_{0} a n d r^{'} = 9 r_{0}$

$a^{'} = a_{0} a n d r^{'} = r_{0}$

answer is B.

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Detailed Solution

$T = \frac{m V^{2}}{R}, a n d T = m g$

$\begin{array}{l} \frac{m v_{0}^{2}}{r_{0}} = m g (v = v_{0}, r = r_{0}) \\ \frac{m {(3 v_{0})}^{2}}{r'} = m g \\ r' = 9 r_{0} \end{array}$
$a_{0} = \frac{v_{0}^{2}}{r_{0}}$
$a' = \frac{{(3 v_{0})}^{2}}{9 r_{0}}$
$= a' = a_{0}$

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