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Physics · UNITS AND MEASUREMENT
हिन्दीIn a new system of units, the unit of mass is chosen as \( \alpha\text{ kg} \), the unit of length as \( \beta\text{ m} \), and the unit of time as \( \gamma\text{ s} \). The magnitude of a energy of \( 4.2\text{ J} \) in this new system of units will be:
Correct answer · Option 1
\( 4.2 \, \alpha^{-1} \beta^{-2} \gamma^2 \)
Explanation
Dimension of energy is \( [\text{M L}^2 \text{T}^{-2}] \). Using \( n_1 U_1 = n_2 U_2 \), \( n_2 = 4.2 (\frac{1}{\alpha})^1 (\frac{1}{\beta})^2 (\frac{1}{\gamma})^{-2} = 4.2 \, \alpha^{-1} \beta^{-2} \gamma^2 \).
