Question

From the dimensional consideration, which of the following equation is correct

• A. T = $2\pi \sqrt{\frac{R^3}{GM}}$
• B. T =2$\pi \sqrt{\frac{GM}{R^3}}$
• C. T =2$\pi \sqrt{\frac{GM}{R^2}}$
• D. T =2$\pi \sqrt{\frac{R^2}{GM}}$

Answer 1

The correct option is A T = $2\pi \sqrt{\frac{R^3}{GM}}$

By substituting the dimension in T = 2$\pi \sqrt{\frac{R^3}{GM}}$
we get $\sqrt{\frac{L^3}{M^{-1}{L}^3{T}^{-2}\times M}}$ =T