Question

TWO VESSELS A AND B OF CROSS-SECTION CONTAIN A LIQUID UPTO THE SAME HEIGHT . AS THE TEMPERATURE RISES , THE LIQUID PRESSURE AT THE BOTTOM WILL :
( VESSEL A IS NARROW AT THE TOP AND BROADER AT THE BOTTOM ; VESSEL B IS NARROW AT THE BOTTOM AND BROAD AT THE TOP )

1. INCREASE IN B , DECREASE IN A
2. INCREASE IN A , DECREASE IN B
3. DECREASE IN BOTH A AND B
4. INCREASE IN BOTH A AND B

Answer 1

Answer on Question #41065, Physics, Mechanics | Kinematics | Dynamics

TWO VESSELS A AND B OF CROSS-SECTION CONTAIN A LIQUID UPTO THE SAME HEIGHT. AS THE TEMPERATURE RISES, THE LIQUID PRESSURE AT THE BOTTOM WILL: ( VESSEL A IS NARROW AT THE TOP AND BROADER AT THE BOTTOM ; VESSEL B IS NARROW AT THE BOTTOM AND BROAD AT THE TOP )

1. INCREASE IN B, DECREASE IN A

2. INCREASE IN A, DECREASE IN B

3. DECREASE IN BOTH A AND B

4. INCREASE IN BOTH A AND B

**Solution**

The liquid pressure at the bottom is

$$p = \rho g h.$$

As the temperature rises, the density $\rho$ decreases, height $h$ increases. In A, the top cross-section is smaller. So, $h$ increase dominates. The case of B is opposite to that of A (density decrease dominates).

Answer: 2. INCREASE IN A, DECREASE IN B.

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