Question

Due to thermal expansion, with rise in temperature:

• A. metallic scale reading becomes lesser than true value (if $\alpha$ of metal scale is greater than that of the object).
• B. pendulum clock becomes slower.
• C. a floating body sinks a little more (assuming temperature of liquid remains same).
• D. apparent weight of a body completely immersed in a liquid increases (assuming temperature of liquid remains same).

Answer 1

Answer: (A), (B)

The correct options are
A metallic scale reading becomes lesser than true value (if $\alpha$ of metal scale is greater than that of the object).
B pendulum clock becomes slower.

(a) True value $=\text{scale reading}\times [1+({\alpha }_s-\alpha \left)\right({\theta }^{\prime }-\theta \left)\right]$
where ${\alpha }_s$ is the coefficient of thermal expansion of the scale and $\alpha$ of the object.
Now, ${\alpha }_s>\alpha$ & ${\theta }^{\prime }>\theta$ [given]
On increasing temperature, the distance between the gradations of metallic scale will increase and hence the measured value will be lower than actual value.
(b) For pendulum clock, $T=2\pi \sqrt{\frac{l}{g}}$​​. On heating, since $l$ increases, time period will increase and clock will become slower.
(c) With rise in temperature, density of a body decreases. Hence a floating body sinks a little less.
(d) Since due to thermal expansion, volume of the body will increase and hence the volume of water displaced by the body will also increase. Thus, force of buoyancy on the body will also increase and hence its apparent weight will decrease.
Only option (a), (b) are correct.