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Physics · UNITS AND MEASUREMENT
हिन्दीIn a new system of units, the unit of mass is \( \alpha\text{ kg} \), the unit of length is \( \beta\text{ m} \), and the unit of time is \( \gamma\text{ s} \). The numerical value of \( 1\text{ Joule} \) of energy in this new system is:
Correct answer · Option 1
\( \alpha^{-1}\beta^{-2}\gamma^2 \)
Explanation
Energy has dimensions \( [M L^2 T^{-2}] \). Using \( n_2 = n_1 (\frac{M_1}{M_2})^1 (\frac{L_1}{L_2})^2 (\frac{T_1}{T_2})^{-2} = 1 \cdot (\alpha)^{-1} (\beta)^{-2} (\gamma)^2 = \alpha^{-1}\beta^{-2}\gamma^2 \).
