A calorie is a unit of heat (about $4.2 ext{ J}$, where $1 ext{ J} = 1 ext{ kg m}^2 ext{ s}^{-2}

Question

A calorie is a unit of heat (about $4.2	ext{ J}$, where $1	ext{ J} = 1	ext{ kg m}^2	ext{ s}^{-2}$). Suppose we employ a new system of units where the unit of mass is $\alpha	ext{ kg}$, unit of length is $\beta	ext{ m}$, and unit of time is $\gamma	ext{ s}$. The magnitude of a calorie in this new system is:

Professor PC Thomas Classes · Answer

Using $n_1 u_1 = n_2 u_2$, we get $n_2 = n_1 [\frac{M_1}{M_2}] [\frac{L_1}{L_2}]^2 [\frac{T_1}{T_2}]^{-2} = 4.2 [\frac{1}{\alpha}] [\frac{1}{\beta}]^2 [\frac{1}{\gamma}]^{-2} = 4.2 \alpha^{-1} \beta^{-2} \gamma^2$.