# A physical quantity of the dimensions of length that can be formed out of c, G and  is (c is velocity of light, G is universal constant of gravitation and e is charge)

To solve these questions first write dimentions of all the given quantity in term of fundamental quantity and then find relation between them.

$\dpi{100} \therefore T= 2\pi \sqrt{l/g}$

- wherein

$\dpi{100} T= time \: period$

$\dpi{100} l= length$

$\dpi{100} g=\: acceleration \: due\: to\: gravity$

$\frac{e^{2}}{4\pi\epsilon _{^{\circ}} }= [F \times d^{2}]= Mc^{3}T^{-2}$

$G= ML^{3}T^{-2}$

$C= L^{-1}$

$l\propto(\frac{e^{2}}{4\pi \epsilon _{^{\circ}}})^{P}G^{q}C^{r}$

$[L^{1}]= [MC^{3}T^{-2}]^{P} [M^{-1}L^{3}T^{-2}]^{q} [LT^{-1}]^{r}$

on comparing both sides we get

$P=\frac{1}{2}, q=\frac{1}{2}, r =-2$

$\therefore l= \frac{1}{C^{2}}[ \frac{Ge^{2}}{4\pi \epsilon _{^{\circ}}} ]^{1/2}$

Exams
Articles
Questions