A) \[[{{h}^{1}}{{c}^{1}}{{G}^{-1}}]\]
B) \[[{{h}^{1/2}}{{c}^{1/2}}{{G}^{-1/2}}]\]
C) \[[{{h}^{1}}{{c}^{-3}}{{G}^{-1}}]\]
D) \[[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]
Correct Answer: D
Solution :
Key Idea: Every equation relating physical quantities should be in dimensional balance. In order to establish relation among various physical quantities, let a, b, c be the powers to which h, c and G are raised, then \[[L]=[h{{\,}^{a}}{{c}^{b}}{{G}^{c}}]\] Putting the dimensions on RHS of above equation, we get \[[L]=[M{{L}^{2}}{{T}^{-1}}]{{\,}^{a}}{{[L{{T}^{-1}}]}^{b}}{{[M{{L}^{-1}}{{L}^{3}}{{T}^{-2}}]}^{c}}\] \[[L]=[{{M}^{a-c}}{{L}^{2a+b+3c}}{{T}^{-a-b-2c}}]\] Comparing the power, we get \[a-c=0\] ?(i) \[2a+b+3c=1\] ?(ii) \[-a-b-2c=0\] ?(iii) Solving Eqs. (i), (ii) and (iii), we get \[a=\frac{1}{2},b=\frac{-3}{2},c=\frac{1}{2}\] Hence, \[[L]=[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]
You need to login to perform this action.
You will be redirected in
3 sec
