Question

Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08mm when the rod is heated from $0^{\circ }$C to ${100}^{\circ }$C. A flask made of the same glass as that of rod measures a volume of 1000 cc at $0^{\circ }$C. The volume it measures at ${100}^{\circ }$C in cc is

• A. 1002.4
• B. 1004.2
• C. 1006.4
• D. 1008.2

Answer 1

The correct option is A 1002.4

$\gamma =\frac{V_2-V_1}{V_1(T_2-T_1)};\alpha =\frac{l_2-l_1}{l_1(T_2-T_1)}$

$T_1=0^{\circ }C,T_2={100}^{\circ }C$

$\gamma =\frac{V_2-V_1}{100V_1};\alpha =\frac{l_2-l_1}{100l_1}$

$l_1$ = 10cm; $l_2-l_1$ = 0.08mm = 0.008cm

$\alpha =\frac{0.008}{10\times 100}=8\times {10}^{-6}{/}^{\circ }C;\gamma =3\alpha =24\times {10}^{-6}{/}^{\circ }C$
$\therefore 24\times {10}^{-6}=\frac{V_2-1000}{1000\times 100}$

$V_2-1000=24\times {10}^{-6}\times {10}^5=2.4\therefore V_2=1002.4cc$