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Physics · UNITS AND MEASUREMENT
हिन्दीThe energy \( E \) of a damped oscillator is given by \( E = \frac{1}{2} m v^2 e^{-b t / m} + \frac{1}{2} k x^2 \), where \( m \) is mass, \( v \) is velocity, \( t \) is time, and \( x \) is displacement. For this equation to be dimensionally consistent, the dimensional formula of the damping constant \( b \) must be:
Correct answer · Option 1
\( [\text{M T}^{-1}] \)
Explanation
The exponent of the exponential function must be dimensionless: \( [\frac{bt}{m}] = [1] \implies [b] = [\frac{m}{t}] = [\text{M T}^{-1}] \).
