A cylindrical metal rod $M$ stands on the table. Also standing on the table is a cylinder $L$ containing a liquid. The cylinder $L$ is made of a glass called "invar", which does not expand or contract on change in temperature. Suppose the temperature of the room is increased with corresponding uniform increase in temperature of both systems $L$ and $M .$ Both the metal and the liquid undergo expansion with increase in temperature.

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The pressure at the bottom of the liquid in $L$ will remain unchanged as the temperature changes

The pressure at the bottom of $M$ will decrease slightly as the rod expands

The pressure at the bottom of $M$ will remain exactly same as the rod gets longer

The pressure at the bottom of the liquid in $L$ will increase as the temperature increases

answer is B, D.

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Detailed Solution

$F o r c y l i n d e r M, P = \frac{W e i g h t}{B a s e a r e a} . W e i g h t r e m a i n s u n c h a n g e d a n d b a s e a r e a i n c r e a s e s w i t h r i s e i n t e m p e r a t u r e . F o r t h e l i q u i d L, i n i t i a l p r e s s u r e P_{i} = ρ g h a n d f i n a l p r e s s u r e P_{f} = \frac{ρ}{(1 + α . △ T)} \times g \times h (1 + α . △ T) = ρ g h$