Q. A calorie is a unit of heat and equal 4.2 J. Suppose we employ a system of units in which the unit of mass is $\alpha$kg, the unit of length is $\beta$ metre and the unit of time is $\gamma$ sec. In this new system. 1 calorie =
A) $\alpha^{- 1}\beta^{- 2}\gamma^{2}$
B) $4.2\alpha\beta^{2}\gamma^{2}$
C) $\alpha\beta^{2}\gamma^{2}$
D) $4.2\alpha^{- 1}\beta^{- 2}\gamma^{2}$
Explanation
[Calorie]=[$ML^{2}T^{- 2}$] Comparing with general dimensional formula $\left\lbrack M^{a}L^{b}T^{c} \right\rbrack,$ we get $a = 1,b = 2,c = - 2$. $n_{2} = 4.2\left\lbrack \frac{1kg}{\alpha kg} \right\rbrack^{1}\left\lbrack \frac{1m}{\beta m} \right\rbrack^{2}\left\lbrack \frac{1s}{\gamma s} \right\rbrack^{- 2}$=4.2$\alpha^{- 1}\beta^{- 2}\gamma^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.