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For the arrangement shown in figure, initially the balance A and B reads $F_{1}$ and $F_{2}$ respectively and $F_{1} > F_{2}$ . Finally when the block is immersed in the liquid then the readings of balance A and B are $f_{1}$ and $f_{2}$ respectively. Identify the statement which is not always (where, F is some force) correct statement.

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$f_{1} > f_{2}$

$F_{1} + F > F_{2} + F$

$f_{1} + f_{2} = F_{1} + F_{2}$

None of these

answer is C.

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Detailed Solution

$F_{1}$ will decrease and $F_{2}$ will increase. So $f_{1}$ may or may not be greater than $f_{2}$ .

If m and $m_{1} b e t h e m a s s e s o f t h e b l o c k a n d t h e l i q u i d r e s p e c t i v e l y a n d σ$ and $ρ$ be the density of the block and the liquid ,

then $F_{1} = m g a n d F_{2} = m_{1} g . A l s o f_{1} = m g (1 - \frac{ρ}{σ}) a n d f_{2} = m_{1} g (1 + \frac{ρ}{σ}) .$

Hence , $f_{1} + f_{2} = F_{1} + F_{2}$

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