Answer:
Option A,C,D
Explanation:
$M\propto h^{a}c^{b}G^{c}$
$M^{-1}\propto(ML^{2}T^{-1})^{a}(LT^{-1})^{b}(M^{-1}L^{3}T^{-2})^{c}$
$\propto M^{a-c}L^{2a+b+3c}T^{-a-b-2c}$
a-c=1 ......(i)
2a+b+3c=0 ........(ii)
a+b+2c=0 ......(iii)
Onsolving (i), (ii) (iii) , $a=\frac{1}{2},b=+\frac{1}{2},c=-\frac{1}{2}$
$\therefore$ $M\propto \sqrt{c}$ only → (a) is correct.
In the same way we can find that,
$L\propto h^{1/2}h^{-3/2}G^{1/2}$
$L\propto \sqrt{h}$ , $L\propto \sqrt{G}$ → (c), (d) are also correct.
