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A balance is made of a rigid rod free to...

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 left pan, it is balanced by a mass `m_(1)` placed in the right pan and similarly when the mass `m` is placed in the right pan, it is balanced by a mass `m_(2)` in the left pan. Neglecting the masses of the pans, `m` is

A

`(m_(1)+m_(2))/(2)`

B

`sqrt(m_(1)m_(2))`

C

`(sqrt(m_(1)^(2)+m_(2)^(2)))/(2)`

D

`sqrt(((m_(1)^(2)+m_(2)^(2)))/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B

Let `L` be the length of the rod and knife edge is placed at a distance `x` from the left pan
About the knife edge
`mg(x)=m_(1)g(L-x)`………..(`1`)
`m_(2)g(x)=mg(L-x)`………..(`2`)
dividing (`1`) by (`2`)
`(m)/(m_(2))=(m_(1))/(m)impliesm=sqrt(m_(1)m_(2))`
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