1.Units, Dimensions and Measurement
hard

If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} $ . It is observed that the time period is directly proportional to $\sqrt {\frac{d}{s}} $ . The value of $b$ should therefore be

A$\frac{3}{4}$
B$\sqrt 3 $
C$\frac{3}{2}$
D$\frac{2}{3}$
(JEE MAIN-2013)

Solution

$T=\sqrt{\left(M L^{-3}\right)^{a} r^{b}[M T^ {-2}] c}$
$= \sqrt{M L^{-3} \quad L^{b} \quad M^{-1} T^{+2}}$
$b-3=0$
$b=3$
Standard 11
Physics

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