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1.Units, Dimensions and Measurement
normal
The time period of a body undergoing simple harmonic motion is given by $T=p^{a} D^{b} S^{c}$, where $p$ is the pressure, $D$ is density and $S$ is surface tension. The values of $a, b$ and $c$ respectively are
A
$1, \frac{1}{2}, \frac{3}{2}$
B
$\frac{3}{2},-\frac{1}{2}, 1$
C
$1,-\frac{1}{2}, \frac{3}{2}$
D
$-\frac{3}{2}, \frac{1}{2}, 1$
Solution
$(d)$ Given, $T=p^{a} D^{b} \rho^{c} S$
Using dimension equation concept, we get $[T]=\left[ ML ^{-1} T ^{-2}\right]^{ a }\left[ ML ^{-3} T ^{0}\right]^{b}\left[ ML ^{0} T ^{-2}\right]^{c}$
Comparing powers, we get
$a+b+c=0$
$-a-3 b=0$
$-2 a-2 c=1$
On solving Eqs. $(i), (ii)$ and $(iii)$, we get
$a=-\frac{3}{2}, b=\frac{1}{2}, c=1$
Standard 11
Physics
