| Of the following quantities which one has the dimensions different from the remaining three? |
| (i) Energy density |
| (ii) Force per unit area |
| (iii) Product of charge per unit volume and voltage |
| (iv) Angular momentum per unit mass |
A) (i)
B) (ii)
C) (iii)
D) (iv)
Correct Answer: D
Solution :
[d]: Energy density \[=\frac{\text{Energy}}{\text{Volume}}=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[{{L}^{3}}]}=[M{{L}^{-1}}{{T}^{-2}}]\] \[=\frac{\text{Force}}{\text{Area}}=\frac{[ML{{T}^{-2}}]}{[{{L}^{2}}]}=[M{{L}^{-1}}{{T}^{-2}}]\] \[\frac{\text{Charge}}{\text{Volume}}\times \text{Voltage}=\frac{\text{Charge}}{\text{Volume}}\times \frac{\text{Work}}{\text{Charge}}\] \[=\frac{\text{Work}}{\text{Volume}}\text{=}\frac{[M{{L}^{2}}{{T}^{-2}}]}{[{{L}^{3}}]}=[M{{L}^{-1}}{{T}^{-2}}]\] \[\frac{\text{Angular momentum}}{\text{Mass}}\text{=}\frac{[M{{L}^{2}}{{T}^{-1}}]}{[M]}=[{{M}^{0}}{{L}^{2}}{{T}^{-1}}]\] Therefore, dimensions of (iv) is different.
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