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A balance is made of a light rigid rod free to rotate about a point not at the centre of the rod. When as known mass x is placed in the left pan, it is balanced by a mass y placed in the right pan. Similarly when the mass x is placed in the right pan, it is balanced by a mass z in the left pan. Neglecting the masses of the pans, x is

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$\frac{y + z}{2}$

$\sqrt{yz}$

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

$\frac{2 yz}{y + z}$

answer is B.

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Detailed Solution

Mechanical advantage

By principle of moments,
F₁ d₁ = F₂ d₂

$\Rightarrow {xd}_{1} = {yd}_{2}$

$Also, {zd}_{1} = {xd}_{2}$

$\Rightarrow \frac{x}{z} = \frac{y}{x} \Rightarrow x = \sqrt{yz}$

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