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The period of a body under S.H.M. is rep...

The period of a body under `S.H.M.` is represented by `TpropP^(a)D^(b)S^(c),` where `P` is the pressure, `D` is the density and `S` is surface tension then the values of `a,b` and `c` are :

A

`1,2,(1)/(3)`

B

`(-3)/(2),(1)/(2),1`

C

`-1,-2,3`

D

`(-1)/(2),(-3)/(2),(-1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`TpropP^(a)D^(b)S^(c)`
`M^(0)L^(0)T^(1)prop[ML^(-1)T^(-2)]^(a)[ML^(-3)]^(b)[ML^(0)T^(-2)]^(C)`
`M^(0)L^(0)TpropM^(a+b+c)L^(-a-3b)T^(-2a-2c)`
Comparing dimensions on both sides,
`a+b+c=0…(i)`
`-a-3b=0…(ii)`
`-2a-2c=1…(iii)`
`(ii)+3(i)` gives `2a+3c=0`...`(iv)`
Now `(iii) + (iv)` gives `c=1`
`:.-2a-2xx1=1impliesa=-3//2`
from `(i),-(3)/(2)+b+1=0impliesb=(1)/(2)`
`:.` The correct choice is `(b)`.
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