If the velocity of light c ,gravitational constant G, planks constant H,are fundamental then dimensional of mass will be
Answers
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: