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Question

The time period of a body in SHM is represented by To=PaρbSc, where P is pressure, ρ is density and S is surface tension. The value of a,b and c respectively for the relation to be dimensionally correct is

A
32,12,1
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B
1,2,3
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C
12,32,12
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D
1,2,13
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Solution

The correct option is A 32,12,1
Dimensional formula of,
Time period, To
[To]=[M0L0T1]
Pressure, P
[P]=[M1L1T2]
Density, ρ
[ρ]=[M1L3T0]
Surface Tension, S
[S]=[M1L0T2]
Now,
[To]=[PaρbSc]
[M0L0T1]=[M1L1T2]a×[M1L3T0]b×[M1L0T2]c
[M0L0T1]=[M(a+b+c)L(a3b+0)T(2a+02c)]
On comparing we get,
a+b+c=0, .............(1)
a3b=0, .............(2)
2a2c=1 .............(3)
On putting the value of c from (1) in (3), we get, b=12
On putting the value of b in (2), we get,
a=32
On putting the value of a in (3), we get,
c=1
Hence, the value of a,b and c is 32,12 and 1

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