Physical World Units and Measurements - Result Question 19
19. The ratio of the dimension of Planck’s constant and that of the moment of inertia is the dimension of
[2005]
(a) time
(b) frequency
(c) angular momentum
(d) velocity
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Answer:
Correct Answer: 19. (b)
Solution:
- (b) Dimension formula for the planck’s constant, $h=[ML^{2} T^{1}]$
Dimension formula for the moment of inertia, $I=[ML^{2}]$
So, the ratio between the plank’s constant and moment of inertia is
$\Rightarrow \frac{h}{I}=\frac{[ML^{2} T^{-1}]}{[ML^{2}]} \Rightarrow[T^{-1}]$
$\Rightarrow \frac{h}{I}=[T^{-1}] \Rightarrow$ dimension of frequency
20
(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 $\frac{[MLT^{-2}][L^{2}]}{[M][M]}$
$ =[M^{-1} L^{3} T^{-2}] $
