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  4. The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs 4 kg. The same object when placed in the right pan of the balance weighs 9 kg. The actual (or) true mass of the object is

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Q. The two arms of a balance are of unequal length. An object when placed in the left pan of the balance weighs $4 \,kg$. The same object when placed in the right pan of the balance weighs $9 \,kg$. The actual (or) true mass of the object is

Solution:

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$m_0 l_1 = m_1 l_2\,\,....(i)$
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$m_2l_1 = m_0 l_2\,\,\,...(ii)$
Dividing $(i)$ by $(ii)$
$⇒ m_0^2 = m_1m_2$
$⇒ m_0 = \sqrt{m_1m_2}$
$=\sqrt{4\times 9}$
$= 6\,kg$