Physical World Units And Measurements Ques 1
1. The dimensions of universal gravitational constant is
[2004]
(a) $\left[\mathrm{M}^{-2} \mathrm{L}^2 \mathrm{T}^{-1}\right]$
(b) $\left[\mathrm{M}^{-1} \mathrm{L}^3 \mathrm{T}^{-2}\right]$
(c) $\left[\mathrm{ML}^2 \mathrm{T}^{-1}\right]$
(d) $\left[\mathrm{M}^{-2} \mathrm{L}^3 \mathrm{T}^{-2}\right]$
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Answer:
Correct Answer: 1.(b)
Solution: (b) $F=\frac{G M_1 m_2}{r^2} \Rightarrow G=\frac{F r^2}{M_1 m_2}$
$\therefore$ dimension of G is $\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{[\mathrm{M}][\mathrm{M}]}$
$ =\left[\mathrm{M}^{-1} \mathrm{L}^3 \mathrm{T}^{-2}\right] $
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