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Physics · UNITS AND MEASUREMENT
हिन्दीThe SI unit of energy is \( \text{J} = \text{kg m}^2 \text{ s}^{-2} \). A student proposes four different expressions for a physical quantity \( Q \) which has the dimensions of energy: (a) \( Q_1 = m^2 v^3 t^{-1} \) (b) \( Q_2 = \frac{1}{2} m v^2 \) (c) \( Q_3 = m a x \) (d) \( Q_4 = m v t \) where \( m \) is mass, \( v \) is speed, \( a \) is acceleration, \( x \) is position, and \( t \) is time. Which of the following options lists ALL expressions that are dimensionally CONSISTENT with energy?
Correct answer · Option 1
\( (b) \) and \( (c) \) only
Explanation
Energy has dimensions \( [M L^2 T^{-2}] \). Checking each:
\( [Q_2] = [M][L T^{-1}]^2 = [M L^2 T^{-2}] \)
\( [Q_3] = [M][L T^{-2}][L] = [M L^2 T^{-2}] \).\nThus, (b) and (c) are dimensionally consistent with energy.
