Question

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.

• A. The pressure at the bottom of $M$ will remain exactly same as the rod gets longer
• B. The pressure at the bottom of $M$ will decrease slightly as the rod expands
• C. The pressure at the bottom of the liquid in $L$ will increase as the temperature increases
• D. The pressure at the bottom of the liquid in $L$ will remain unchanged as the temperature changes.

Answer 1

Answer: (B), (D)

The correct options are
B The pressure at the bottom of $M$ will decrease slightly as the rod expands
D The pressure at the bottom of the liquid in $L$ will remain unchanged as the temperature changes.

Pressure at bottom is $P=\frac{\text{Weight}}{\text{Base area}}$
Now as the temperature increases, metal rod expands. As a result base area increases.Hence pressure at bottom of $M$ decreases.
As the temperature increases, liquid in the $L$ expands but there will be no change in base area as $L$ is made of invar.
Hence, the pressure at the bottom of the liquid in $L$ will remain unchanged.