A) 9%
B) \[9.3\times {{10}^{-11}}%\]
C) 10%
D) none of these
Correct Answer: B
Solution :
Heat taken by the given body \[=mc\,\Delta \,\theta \] {specific heat of body \[=0.2\,kcal\text{/}kg{}^\circ C,\] final temperature of the body\[=100{}^\circ C\]} \[\Delta E=m\times 0.2\times 100\] \[=20\,m\,kcal\] \[=20\,m\times 4.2\times {{10}^{3}}J\] Now gain in mass is given by \[\Delta m=\frac{\Delta E}{{{c}^{2}}}\] (\[\because E=m{{c}^{2}}\]) \[=\frac{20\,m\,\times 4.2\,\times {{10}^{3}}}{{{(3\times {{10}^{8}})}^{2}}}\] Therefore, percentage increase in mass is given by \[=\frac{\Delta m}{m}\times 100\] \[=\frac{20\,m\times 4.2\times {{10}^{3}}}{{{(3\times {{10}^{8}})}^{2}}\times m}\times 100\] \[=9.3\times {{10}^{-11}}%\]
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