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If the energy, E = G^p h^q c^r, where G ...

If the energy, `E = G^p h^q c^r,` where G is the universal gravitational constant, h is the Planck's constant and c is the velocity of light, then the values of p, q and r are, respectively

A

`-1//2,1//2 and 5//2`

B

`1//2,-1//2 and -5//2`

C

`-1//2, 1//2 and 3//2`

D

`1//2, -1//2 and -3//2`

Text Solution

Verified by Experts

The correct Answer is:
A
`E=G^(p)h^(q)c^(r)` . . . (i)
`[M^(1)L^(2)T^(-2)]=[M^(-1)L^(3)T^(-2)]^(p)[ML^(2)T^(-1)]^(q)[LT^(-1)]^(r)`
`[M^(-p+q)L^(3p+2p+r)T^(-2p-q-r)]`
Applying principle of homogeneity of dimenions, we get
`-p+q=1` . . .(ii) ltBrgt `3p+2q+r=2` . . . (iii)
`2p-q-r=-2` . . .(iv) ltbr. Adding (iii) and (iv), we get `p+q=0`
Adding (ii) and (v), we get `q=(1)/(2)`
From (ii), we get `p=q-1=(1)/(2)-1=-(1)/(2)`
Put in (iii), we get `-(3)/(2)+1+r=2,r=(5)/(2)`.
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