Physics - Unit & Dimension Question with Solution | TestHub

$$\boxed{f=\sqrt{\frac{h{c}^5}{G}}}$$

We need the **dimensions of $f$**.

### Step 1: Dimensions of $h,c,G$

$$[h]=M{L}^2{T}^{-1}$$

$$[c]=L{T}^{-1}$$

Therefore,

$$[c^5]=L^5{T}^{-5}$$

Also,

$$[G]=M^{-1}{L}^3{T}^{-2}$$

### Step 2: Substitute dimensions

$$[f]=\sqrt{\frac{(M{L}^2{T}^{-1})(L^5{T}^{-5})}{M^{-1}{L}^3{T}^{-2}}}$$

Simplify:

$$[f]=\sqrt{\frac{M{L}^7{T}^{-6}}{M^{-1}{L}^3{T}^{-2}}}$$

$$[f]=\sqrt{M^2{L}^4{T}^{-4}}$$

Hence,

$$\boxed{[f]=M{L}^2{T}^{-2}}$$

✅ Final Answer

$$\boxed{M{L}^2{T}^{-2}}$$

This is the dimension of energy