First slide

Dimensions of physical quantities

Question

From the dimensional consideration, which of the following equation is correct?
T- time period
G- universal gravitational constant
M- mass of earth

Easy

A

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$
B

$T = 2 π \sqrt{\frac{G M}{R^{3}}}$
C

$T = 2 π \sqrt{\frac{G M}{R^{2}}}$
D

$T = 2 π \sqrt{\frac{R^{2}}{G M}}$

Solution

By substituting the dimensions in $T = 2 π \sqrt{\frac{R^{3}}{G M}}$
we get $\sqrt{\frac{L^{3}}{M^{- 1} L^{3} T^{- 2} \times M}} = T$

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