Question:medium
Time period of a particle is \( T = k\sqrt{\frac{\rho r^3}{\sigma}} \), where \( k \) is a dimensionless constant, \( \rho \) is density, and \( r \) is radius. The dimension of \( \sigma \) is same as
Time period of a particle is \( T = k\sqrt{\frac{\rho r^3}{\sigma}} \), where \( k \) is a dimensionless constant, \( \rho \) is density, and \( r \) is radius. The dimension of \( \sigma \) is same as
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This formula $T \propto \sqrt{\rho r^3/\sigma}$ specifically relates to the time period of oscillation of a liquid drop, where restoring forces are provided by surface tension $\sigma$. Knowing standard physical formulas can serve as a quick sanity check.
Updated On: Apr 21, 2026
- surface tension
- restoring force
- coefficient of viscosity
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The Correct Option is A
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