If the length of a cylinder on heating increases by 2%, the area of its base will increase by:

0.5%

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Solution

The correct option is D 4%
change in length due to thermal expansion,
$\frac{Δ l}{l} = α_{l} Δ T$ . . . .(1)
Change in area due to thermal expansion,
$\frac{Δ A}{A} = α_{A} Δ T$ . . . . .(2)
We know that $α_{A} = 2 α_{l}$
equation (2) become,
$\frac{Δ A}{A} = 2 α_{l} Δ T$
$\frac{Δ A}{A} = 2. \frac{Δ l}{l}$ (from equation 1)
Given, $\frac{Δ l}{l} = 2$ %
$\frac{Δ A}{A} = 2 \times 2 = 4$ %
The correct option is D.

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If the length of a cylinder on heating increases by 2%, the area of its base will increase by:

The correct option is D 4%change in length due to thermal expansion,Δll=αlΔT. . . .(1)Change in area due to thermal expansion,ΔAA=αAΔT. . . . .(2)We know that αA=2αlequation (2) become,ΔAA=2αlΔTΔAA=2.Δll (from equation 1)Given,Δll=2%ΔAA=2×2=4%The correct option is D.