Question

A calorie is a unit of heat or energy and it equals about $4.2J$ where $1J=1kg{m}^2{s}^{-2}$. Suppose we employ a system of units in which the unit of mass equals $\alpha kg,$ the unit of length equals $\beta m$, the unit of time is $\gamma s,$ then the magnitude of calorie in the new units is $\mathrm{4.2.}{\alpha }^x\cdot {\beta }^y\cdot {\gamma }^2$ such that

• A. $x=1,y=2,z=-2$
• B. $x=-1,y=-2,z=+2$
• C. $x=1,y=-2,z=+2$
• D. $x=-1,y=2,z=+2$

Answer 1

Answer: (B)

$1$ calorie $=4.2kg{m}^2{s}^{-2}$
As $n_1{u}_1=n_2{u}_2$
$4.2kg{m}^2{s}^{-2}=\left(n_2\right)(\alpha kg)(\beta m{)}^2(\gamma s{)}^{-2}$
$\Rightarrow 4.2kg{m}^2{s}^{-2}=\left(n_2\right)\left(\alpha \cdot {\beta }^2\cdot {\gamma }^{-2}\right)kg{m}^2{s}^{-2}$
or $n_2=4.2{\alpha }^{-1}\cdot {\beta }^{-2}\cdot {\gamma }^2$
$\Rightarrow x=-1,y=-2,z=+2$