Question 59 of 149
Applying the principle of homogeneity of dimensions, determine which one is correct,
where is time period, is gravitational constant, is mass, is radius of orbit.
Show answer and solution
Answer: (C)
According to principle of homogeneity dimension of LHS should be equal to dimensions of RHS so option (3) is correct.
$\begin{aligned}
& \mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{\mathrm{GM}} \\
& {\left[\mathrm{T}^2\right]=\frac{\left[\mathrm{L}^3\right]}{\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right][\mathrm{M}]}}
\end{aligned}$
(Dimension of is )
$\begin{aligned}
& \mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{\mathrm{GM}} \\
& {\left[\mathrm{T}^2\right]=\frac{\left[\mathrm{L}^3\right]}{\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right][\mathrm{M}]}}
\end{aligned}$
(Dimension of is )
