Question

If c the velocity of light, h planck's constant and g gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is:

Answer 1

Explanation:

[m] = c12G − 12h12

Explanation:

Here, [c] = LT − 1

[G] = M − 1L3T − 2

[h] = M1L2T − 1

Let mαcxGyhz

By substituting the dimensions of each quantity in both the sides,

M = (LT − 1) x (M − 1L3T − 2) y (ML2T − 1) z

M = [My + zLx + 3y + 2zTx − 2y − z]

By equating the power of M, L, T in both the sides:

−y + z = 1, x + 3y + 2z = 0, −x − 2y − z = 0

By soling the above equation,

We get, x

Answer 2

Answer:

Answer:

[m]=c12G−12h12

Explanation:

Here, [c]=LT−1

[G]=M−1L3T−2

[h]=M1L2T−1

Let mαcxGyhz

By substituting the dimensions of each quantity in both the sides,

M=(LT−1)x(M−1L3T−2)y(ML2T−1)z

M=[My+zLx+3y+2zTx−2y−z]

By equating the power of M, L, T in both the sides:

−y+z=1,x+3y+2z=0,−x−2y−z=0

By soling the above equation ,

We get, x