Question

A quantity 𝑓 is given by $f=\sqrt{\frac{h{c}^5}{G}}$ where 𝑐 is speed of light, 𝐺 universal gravitational constant and ℎ is the Planck's constant. Dimension of 𝑓 is that of

• A. momentum
• B. area
• C. volume
• D. energy

Answer 1

The correct option is D energy

The dimensions of given quantity is,
Planck's constant $\left[h\right]=M^1{L}^2{T}^{-1}$
Speed of light $\left[c\right]=L^1{T}^{-1}$
Universal gravitational constant $\left[G\right]=M^{-1}{L}^2{T}^{-2}$

According to given formula,
substitute the respective dimensions
$\left[f\right]=\sqrt{\frac{M^1{L}^2{T}^{-1\times L^5{T}^{-5}}}{M^{-1}{L}^3{T}^{-2}}}$

$=M^1{L}^2{T}^{-2}$

Final Answer: (c)