A) \[T=k\sqrt{\rho {{r}^{3}}/S}\]
B) \[T=k\sqrt{{{\rho }^{1/2}}{{r}^{3}}/S}\]
C) \[T=k\sqrt{\rho {{r}^{3}}/{{S}^{1/2}}}\]
D) None of these
Correct Answer: A
Solution :
Let \[T\propto {{S}^{x}}{{r}^{y}}{{\rho }^{z}}\] by substituting the dimension of \[[T]=[T]\] \[[S]=[M{{T}^{-2}}],\,[r]=[L],\,[\rho ]=[M{{L}^{-3}}]\] and by comparing the power of both the sides \[x=-1/2,\,y=3/2,\,z=1/2\] so \[T\propto \sqrt{\rho {{r}^{3}}/S}\Rightarrow T=k\sqrt{\frac{\rho {{r}^{3}}}{S}}\]
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