Question

9.
Planck's constant (h), speed of light in vacuum (c)
and Newton's gravitational constant (G) are three
fundamental constants. Which of the following
combinations of these has the dimension of
length?
[NEET(Phase-2) 2016]​

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: