A calorie is a unit of heat energy and its value is 4.18 J where $1 \mathrm{~J}=1 \mathrm{~kg} \math

Question

A calorie is a unit of heat energy and its value is 4.18 J where $1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-2}$. Suppose we use a new system of units in which unit of mass equals $\alpha \mathrm{kg}$, the unit of length equals $\beta \mathrm{m}$ and the unit of the time is $\gamma \mathrm{sec}$. Then the value of a calorie in the new system of units is\

Professor PC Thomas Classes · Answer

(a) : $1 \mathrm{~J}=(1 \mathrm{~kg})(1 \mathrm{~m})^2(1 \mathrm{sec})^{-2}$ $ \  \begin{array}{ll} & 1 x=(\alpha \mathrm{kg})(\beta \mathrm{m})^2(\gamma \mathrm{sec})^{-2} \ 	herefore & \frac{1 \mathrm{~J}}{1 x}=\left(\frac{1}{\alpha}ight)\left(\frac{1}{\beta}ight)^2(\gamma)^2=\frac{\gamma^2}{\alpha \beta^2} \ 	herefore & 1 \mathrm{~J}=\frac{\gamma^2}{\alpha \beta^2} x 	ext { or } 1 \mathrm{cal}=4.18 \frac{\gamma^2}{\alpha \beta^2} \end{array} \ $