Question

A liquid drop of density `rho` , radius `r`, and surface tension `sigma` oscillates with time period `T` . Which of the following expressions for `T^(2)` is correct?
A. `( rho r^(3))/( sigma)`
B. `( rho sigma)/( r^(3))`
C. `( r^(3) sigma)/( rho)`
D. None of these

Answer 1

Correct Answer - A
Let `T^(2) = rho ^(a) r^(b) sigma^( c )`
`T^(2) = (ML^(-3))^(a) (L) ^(b) (MT^(-2))^( c ) = M^(a + c ) L^(-3a + b) T^(-2 c )`
` a + c = 0 , -3a + b = 0 , and -2c = 2`
Hence , a = 1 , b = 3 , and `c = -1 T^(2) = rho r^(3) sigma^(-1) = (rho r^(3))/(sigma)`