Question

if the energy E= G^p H^q C ^r, where G is universal constant of gravity, H is planks constant and C is velocity of light. Find P,Q,R.​

Answer 1

Answer:

P= -1/2

Q=1/2

R=5/2

Explanation:

dimensions of:

E = [M L^2 T^-2]

G= [M^-1 L^3 T^-2 ]

H= [M L^2 T^−1]

C=[LT^-1]

Equating dimensions of LHS and RHS,

[M L^2 T^-2] =  [M^-1 L^3 T^-2 ]^p [M L^2 T^−1]^q [LT^-1]^r

                     = [M^(-p+q) L^(3p+2q+r) T(-2p-q-r)

Equating powers and applying principle of homogeneity of dimensions, we get  

−p+q=1                  . . . (ii)

3p+2q+r=2            . . . (iii)

−2p−q−r=−2           . . . (iv)

Solving these equations, we get:

p= -1/2

q= 1/2

r= 5/2

HOPE IT HELPS!