Question

if velocity of light c, Planck's constant h and gravitational constant G are taken as fundamental quantities then the dimensions of length will be​

Answer 1

Answer:

we know,

and

we have to write mass in term of c, h and G

so, [M] = k , k is proportionality constant

[M] = [LT^-1]^x[ML²T^-1]^y [M^-1L³T^-2]^z

[M] = [M^(y - z) L^(x + 2y + 3z) T^(-x -y - 2z)]

compare both sides,

y - z = 1

x + 2y + 3z = 0

-x - y - 2z = 0

after solving these equations we get,

x = 1/2 , y = 1/2 and z = -1/2

so, mass =

similarly, we have to write length in term of c , h and G

length = k

[L] = k[M^(y - z) L^(x + 2y + 3z) T^(-x - y - 2z)]

compare both sides,

y - z = 0

x + 2y + 3z = 1

-x - y - 2z = 0

after solving theses equations ,

we get, x = -3/2 , y = 1/2 , z = 1/2

so, length =

again, we have to write time in term of c ,h and G.

Time = k

[T] =k [M^(y-z) L^(x + 2y + 3z) T^(-x - y - 2z)]

compare both sides,

(y - z) = 0

x + 2y + 3z = 0

-x - y - 2z = 1

after solving these equations,

we get, y = z = 1/2 , x = -5/2

so, Time =

Explanation: