Discussion Forum

 Plank's constant h, speed of light c and gravitational constant G are used to form a unit of length  L and a unit of mass M . Then, the correct option is /are

Answer:

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.