MCQ
The dimensions of universal gravitational constant are
- A$M^{-2} L^2 T^{-2}$
- ✓$M^{-1} L^3 T^{-2}$
- C$M L^{-1} T^{-2}$
- D$M L^2 T^{-2}$
✓
Answer
Correct option: B.
$M^{-1} L^3 T^{-2}$
(b)
$F=\frac{G m_1 m_2}{d^2} \Rightarrow G=\frac{F d^2}{m_1 m_2}$
$\therefore[G]=\frac{\left[M L T^{-2}\right]\left[L^2\right]}{\left[M^2\right]}=\left[M^{-1} L^3 T^{-2}\right]$
$F=\frac{G m_1 m_2}{d^2} \Rightarrow G=\frac{F d^2}{m_1 m_2}$
$\therefore[G]=\frac{\left[M L T^{-2}\right]\left[L^2\right]}{\left[M^2\right]}=\left[M^{-1} L^3 T^{-2}\right]$
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