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

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 value 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^(n) h^(n) c^(r)`.......(i)
`[M^(1)L^(2)T^(-2)]=[M^(-1)L^(3)T^(-2)]^(n) [ML^(2)T^(-1)]^(n)[LT^(-1)]^(r)`
`=M^(p)""^qL^(3p+2q+r)T^(-2p) qr`
Applying principle of homogeneity of dimensions, we get
`-p+q=1......(i)`
`3p+2q+r=2......(iii)`
`-2p-q-r=-2......(iV)`
Add (iii) and (iv), p+q=0
Add (ii) and (v), we get `q=(1)/(2)`
From (ii)(, we get `p=q-1=1/2 =-1/2`
Put in (iii), we get `-3/2+1+r=2, r5//2`
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