Question

A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kgm² s^-2. Suppose we employ a system of units in which the unit of mass equals a kg, the unit of length equals j8 m, the. unit of time is ys. Show that a calorie has a magnitude 4.2  ^{α-1 β-2 γ2} in terms of the new units.

Answer 1

$1kg_{new}=\alpha*1{kg}$

$1{kg}=\frac{1}{\alpha}*1kg_{new}$

$1m_{new}=\beta*1m$

$1m=\frac{1}{\beta}*1m_{new}$

$1m^2=\frac{1}{\beta^2}*1m^2_{new}$

$1s_{new}=\gamma*1s$

$1s=\frac{1}{\gamma}*1s_{new}$

$1s^{-2}={\gamma}^2*1s_{new}$

$4.2J=4.2[kgm^2s^{-2}]=4.2*1kg*1m^2*1s^{-2}=$

$4.2*\frac{1}{\alpha}*1kg_{new}*\frac{1}{\beta^2}*1m^2_{new}*{\gamma}^2*1s_{new}=$

$4.2*{\alpha}^{-1}*{\beta^{-2}}*{\gamma}^2*1kg_{new}*1m^2_{new}*1s_{new}=$

$4.2{\alpha}^{-1}{\beta^{-2}}{\gamma}^2[kg_{new}m^2_{new}s_{new}]$

$\text{Answer:}\ 4.2{\alpha}^{-1}{\beta^{-2}}{\gamma}^2[kg_{new}m^2_{new}s_{new}]$