Question

A calorie is a unit of heat and equals 4.2 J. Suppose we employ a system of units in which of the unit of mass is α kg, the unit of length is β metre and the unit of time is γ second. In this new system, 1 calorie =

• A. α^–1β^–2γ²
• B. 4.2 αβ²γ^–2
• C. αβ²γ^–2
• D. 4.2 α^–1β^–2γ²

Answer 1

Answer: (D)

4.2 α^–1β^–2γ²

Answer 2

4.2 J = n₂ unit n₂ = $4.2\left\lbrack \frac{1kg}{\alpha kg} \right\rbrack^{1}\left\lbrack \frac{1m}{\beta m} \right\rbrack^{2}\left\lbrack \frac{1\sec}{\gamma\sec}^{- 2} \right\rbrack$= $\frac{4.2\gamma^{2}}{\alpha\beta^{2}}$