A meter stick in form of a uniform rod is hinged at a distance x from the centre. It undergoes SHM with a time period of `(2pi)/3 sqrt(7/5)` sec. What is the value of x.

Options

A. `1/18 m `
B. `2/9m `
C. `1/9 m`
D. 10c m

Answer

A

Explanation

`T=2pisqrt(I/(mgx)) =(2pi)/3 sqrt(7/3)`
`sqrt(((ml^(2))/12+mx^(2))/(mgx))=1/3 sqrt(7/5)`
`(l^(2))/12+x^(2) =7/25 xx10x`
`x^(2)-(14x)/9+1/12 =0`
`x=(14/9 pm sqrt(196/81-1/3))/2=(14/9 pm sqrt((196-27)/81))/2`
`=(14/9 pm sqrt(169/81))/2=1/18 m`