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10-1.Thermometry, Thermal Expansion and Calorimetry
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A circular metallic ring of radius $R$ has a small gap of width $d$. The coefficient of thermal expansion of the metal is $\alpha$ in appropriate units. If we increase the temperature of the ring by an amount $\Delta T$, then width of the gap
A
will increase by an amount $d \alpha \Delta T$
B
will not change
C
will increase by an amount $(2 \pi R-d) \alpha \Delta T$
D
will decrease by an amount $d \alpha \Delta T$
(KVPY-2012)
Solution
(a)
Gap or cavity also expands at same rate as that of metal.
Hence, width of gap also increases by same amount.
$\therefore$ Width of gap increases by $\Delta d=d \alpha \Delta T$
Standard 11
Physics
