JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
Applying the principle of homogeneity of dimensions, determine which one is correct. where \(\mathrm{T}\) is time period, \(\mathrm{G}\) is gravitational constant, \(M\) is mass, \(r\) is radius of orbit.
- A \(\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}}{\mathrm{GM}^2}\)
- B \(\mathrm{T}^2=4 \pi^2 \mathrm{r}^3\)
- C \(\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{G M}\)
- D \(\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^2}{G M}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{G M}\)
Step-by-step Solution
Detailed explanation
According to principle of homogeneity dimension of \(LHS\) should be equal to dimensions of RHS so option \((3)\) is correct. \(\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{\mathrm{GM}}\)…
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