State true/false:
`S_1` : Hydrostatic pressure is a scalar quantity even though pressure is force divided by area and force is a vector quantity?
`S_2`: A barometer made of a very narrow tube (see figure) is placed at normal temperature and pressure. The coefficient of volume expansion of mercury is `0.00018//.^@C` and that of the tube is negligible. The temperature of mercury in the barometer is now raised by `1^@C` but the temperature of the atmosphere does not change. Then, the mercury height in the tube remains unchanged.
`S_3` A block of ice with a lead shot embedded in it is floating on water contained in a vessel. The temperature of the system is maintained at `0^@C` as the ice melts. When the ice melts completely the level of water in the vessel rises.

Options

A. TTF
B. TFT
C. TFF
D. TTT

Answer

C

Explanation

`S_(1)` : True
Pressure is always acting normal to hence it is considered as scalar.
`S_(2)` :False
On increasing the temperature of mercury its density. Hence level of mercury in barometer tube will increases.
`S_(3)`: False
When ice melts level of water does not change. in case of lead, it was initially i.e., it would had displaced the water equal to weight of lead. so, volume of water displaced would be
`V_(1)=m/(rho_(w))` (m=mass of lead)
Now, when ice melts lead will sink and it would displace the water equal to volume of lead itself so, volume of water displaced in this case would be
`V_(2)=m/(rho_(l))`
Now, as `rho_(l) gt rho_(w), V_(2) gt V_(1)` or level will fall.