A) \[ML{{T}^{-2}}{{K}^{-1}}\]
B) \[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}\]
C) \[{{M}^{0}}{{L}^{2}}{{T}^{-2}}{{K}^{-1}}\]
D) \[{{M}^{0}}L{{T}^{-2}}{{K}^{-1}}\]
Correct Answer: C
Solution :
The heat energy constant H of a body of mass m at temperature \[\theta \] is given by \[H=ms\theta \] where s is the specific heat. Therefore \[s=\frac{H}{m\theta }\] \[\therefore \] Dimensions of, \[s=\frac{\text{dimensions}\,\text{of}\,\text{heat}\,\text{energy}}{\text{dimension}\,\text{of}\,\text{mass}\,\text{xdimenstion}\,\text{of}\,\text{temperature}}\] \[=-\frac{M{{L}^{2}}{{T}^{-2}}}{M\times K}={{M}^{o}}{{L}^{2}}{{T}^{-2}}{{K}^{-1}}\] Hence, the correction option is (c).
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