OnlineCBT
Physics · UNITS AND MEASUREMENT
हिन्दीThe speed of sound \( v \) in a gas depends on the pressure \( P \) and density \( \rho \) of the gas as \( v = k P^x \rho^y \), where \( k \) is a dimensionless constant. The values of exponents \( x \) and \( y \) are:
Correct answer · Option 1
\( x = \frac{1}{2}, y = -\frac{1}{2} \)
Explanation
Dimensions: \( [v] = [L T^{-1}] \), \( [P] = [M L^{-1} T^{-2}] \), \( [\rho] = [M L^{-3}] \). Equating dimensions: \( [L T^{-1}] = [M^{x+y} L^{-x-3y} T^{-2x}] \). Equating exponents gives \( x + y = 0 \), \( -2x = -1 \implies x = 1/2 \) and \( y = -1/2 \).
