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When a body is weighed successively in t...

When a body is weighed successively in the two pans of a physical balance with unequal arms, the apparent masses are found to be `M_(1)` and `M_(2)`. Show that the length of the arms are in the ratio `sqrt(M_(1)): sqrt(M_(2))`.

Text Solution

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Let `l_(1)` and `l_(2)` be the lengths of left and right arms of the balance.
Then, `l_(1)M=l_(2)M_(1) rArr l_(1)/l_(2)=M_(1)/M`
and `l_(1)M_(2)=l_(2)M rArr l_(1)/l_(2)=M/M_(2)`
or `l_(1)/l_(2)l_(1)/l_(2)=M_(1)/MM/M_(2)=M_(1)/M_(2)`
`:. l_(1)/l_(2)=sqrt(M_(1)/M_(2))`
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