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A balance is made of a rigid rod free to rotate about a point not at the centre of the rod. When an unknown mass m is placed in the right-hand pan, it is balanced by a mass $m_{1}$ in the left hand pan, and similarly when the mass m is placed in the left-hand pan, it is balanced by a mass $m_{2}$ in the right-hand pan. Neglecting the masses of the pans, m is

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$\sqrt{\frac{m_{1}^{2} + m_{2}^{2}}{2}}$

$\frac{\sqrt{m_{1}^{2} m_{2}^{2}}}{2}$

$\sqrt{m_{1} m_{2}}$

$\frac{m_{1} + m_{2}}{2}$

answer is B.

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Detailed Solution

$m g x = m_{1} g y$

$m_{2} g x = m g y$

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