Question

Radius of a sphere is $100cm$ at $0^{o}C$ and $100.1cm$ at ${100}^{o}C$. Coefficient of cubical expansion of the sphere is

• A. $30\times {10}^{-6}/C$
• B. $10\times {10}^{-6}{/}^{o}C$
• C. $60\times {10}^{-6}{/}^{o}C$
• D. $20\times {10}^{-6}{/}^{o}C$

Answer 1

The correct option is A $30\times {10}^{-6}/C$

Given,

$T_0=0^{0}C$

$T_t={100}^{0}C$

$r_0=100cm$

$r_t=100.1cm$

According to thermal expansion,

$l_t=l_0(1+\alpha \Delta T)$

$2\pi r_t=2\pi r_0(1+\alpha \Delta T)$

$r_t=r_0(1+\alpha \Delta T)$

$100.1cm=100cm(1+\alpha \Delta T)$

$\frac{100.1}{100}=1+\alpha ({100}^{0}C-0^{0}C)$

$\alpha =1\times {10}^{-5}{/}^{0}C$

The coefficient of cubical expansion of sphere is three times of linear coefficient of expansion,

$\gamma =3\alpha$

$\gamma =3\times {10}^{-5}=30\times {10}^{-6}{/}^{0}C$

The correct option is A.