1.3 A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where

PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

1 \mathrm{~J}= 1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-2}

. Suppose we employ a system of units in which the unit of mass equals

\alpha

kg , the unit of length equals

\beta \mathrm{m}

, the unit of time is

\gamma \mathrm{s}

. Show that a calorie has a magnitude

4.2 \alpha^{-1} \beta^{-2} \gamma^{2}

in terms of the new units.