99 Percentile Qs Bank for JEE MainPhysicsUnits and Dimensions
If the velocity of light C , the gravitational constant G and Planck's constant h are chosen as the fundamental units, the dimension of density in the new system is
Options
- AC^3 G⁻² h^1
- BC^5 G⁻² h⁻¹
- CC^ -3 / 2 G^ -1 / 2 h^ 1 / 2
- DC^ 9 / 2 G^ -1 / 2 h^ -1 / 2
Correct answer
B. C^5 G⁻² h⁻¹
Step-by-step solution
Let = kC ^ a G ^ b h ^ c aligned & [ ]=[ C ]^ a [ G ]^ b [ h ]^ c & ML ⁻³= L ^ a T ^ - a M ^ - b L ^ 3 ~b ~T ^ -2 ~b M ^ c L ^ 2 c T ^ - c & 1=- b + c ,-3= a +3 ~b +2 c , 0=- a -2 ~b - c & a =5, ~b =-2 and c =-1 aligned