If the period t of a drop of liquid of density d vibrating under surface tension s is given by the formula `t = sqrt(d^(a)r^(b)s^(c ))` where r is radius of drop. a =1 and c = -1, the value of b is

Options

A. 3
B. -3
C. -4
D. 4

Answer

A

Explanation

Time period, `t = sqrt(d^(a)r^(b)s^(c))`
The dimensional formulae of above expression are, `[M^(0)L^(0)T] = sqrt([ML^(-3)]^(a)[L]^(b)[MT^(-2)]^(c))`
`[M^(0)L^(0)T] = [ML^(-3)]^(a//2)[L]^(b//2)[MT^(-2)]^(c//2)`
On compairing coefficients on both sides,
-c = 1
c = -1
`M^(0) = M^(a/2+c/2) implies a/2 +c/2 = 0 implies a = 1`
`L^(0) = L^(-3a/2+b/2) implies -3a/2 +b/2 = 0 implies b = 3`