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Question

Due to thermal expansion, with rise in temperature:

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Solution

The correct options are

**A** metallic scale reading becomes lesser than true value (if α of metal scale is greater than that of the object).

**B** pendulum clock becomes slower.

(a) True value =scale reading×[1+(αs−α)(θ′−θ)]

where αs is the coefficient of thermal expansion of the scale and α of the object.

Now, αs>α & θ′>θ [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=2π√lg. 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.

(a) True value =scale reading×[1+(αs−α)(θ′−θ)]

where αs is the coefficient of thermal expansion of the scale and α of the object.

Now, αs>α & θ′>θ [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=2π√lg. 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.

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