Question

Match the physical quantities given in Column I with suitable dimensions expressed in Column II.

Column I	Column II
a) Angular momentum	1) $M^{-1}{L}^3{T}^{-2}$
b) Torque	2) ${MLT}^{-2}$
c) Gravitational constant	3) ${ML}^2{T}^{-2}$
d) Tension	4) ${ML}^2{T}^{-1}$

• A. a-1, b-3, c-4, d-2
• B. a-1, b-4, c-3 d-2
• C. a-4, b-3, c-1, d-2
• D. a-1, b-2, c-4, d-3

Answer 1

Answer: (C)

a-4, b-3, c-1, d-2

Angular momentum is given by $\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$.

Thus, it's dimensions are $\left[L\right]=L.ML{T}^{-1}=M{L}^2{T}^{-1}$
Torque is given as $\overrightarrow{r}\times \overrightarrow{F}$.

Thus, dimensions are $L.ML{T}^{-2}=M{L}^2{T}^{-2}$.
Tension is force and hence its dimensions are $ML{T}^{-2}$.
Gravitational constant relationship is $F=G\frac{Mm}{r^2}$
Thus, $\left[G\right]=\frac{\left[F\right]\left[r^2\right]}{\left[Mm\right]}=\frac{ML{T}^{-2}.L^2}{M^2}=M^{-1}{L}^3{T}^{-2}$
Thus, option C is correct.