Question

Time period T of a simple pendulum may depend upon mass of the bob m; length of simple pendulum ‘$\ell$ ’ and ‘g’ the acceleration due to gravity as $T\alpha m^a{l}^b{g}^c$. Then the value of a, b and c are:

• A. $-\frac{1}{2},0,\frac{1}{2}$
• B. $\frac{1}{2},0,-\frac{1}{2}$
• C. $0,-\frac{1}{2},\frac{1}{2}$
• D. $0,\frac{1}{2},-\frac{1}{2}$

Answer 1

The correct option is D

$0,\frac{1}{2},-\frac{1}{2}$

$T\alpha \left[M{]}^a\right[L{]}^b[L{T}^{-2}{]}^c$

$T=K[M{]}^a{L}^{b+c}{t}^{-2c}$

$a=0,$ $-2c=1$ $b+c$

$c=-\frac{1}{2}$ $b-\frac{1}{2}=0$

$b=\frac{1}{2}$

$a=0b=\frac{1}{2}c=-\frac{1}{2}$