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Physics · UNITS AND MEASUREMENT
हिन्दीIn deriving the expression for the time period \( T \) of a simple pendulum as \( T = k l^x g^y m^z \) depending on length \( l \), acceleration due to gravity \( g \), and mass \( m \), what are the exponents \( x, y, z \) respectively?
Correct answer · Option 2
\( \frac{1}{2}, -\frac{1}{2}, 0 \)
Explanation
Assuming \( T = k l^x g^y m^z \), dimensional equation is \( [T^1] = [L]^x [L T^{-2}]^y [M]^z = [L^{x+y} T^{-2y} M^z] \). Comparing powers: \( z = 0 \), \( -2y = 1 \implies y = -1/2 \), and \( x + y = 0 \implies x = 1/2 \). Thus, \( x = 1/2, y = -1/2, z = 0 \).
