A spring balance has a scale that reads `0` to `20kg`. The length of the scale is `10cm`. A body suspended from this balance, when displaced and released, oscillates with period of `(pi)/(10)s`. The mass of the body is

Options

A. 350.67 N
B. 540.11 N
C. 311.24 N
D. 300.5 N

Answer

C

Explanation

Time period of the spring mass system,
`T = 2pi sqrt((m)/(k))" "...(i)`
From spring, mg = kx
`rArr" "k=(mg)/(x)=(60 xx 9.8)/(30 xx 10^(-2))=1960 Nm^(-1)" "...(ii)`
From Eqs. (i) and (ii), we get
`0.8 = 2pi sqrt((m)/(1960))`
`rArr" "(0.8 xx 0.8 xx 1960)/(4 pi^(2))=m`
`m = 31.81 kg" "rArr" "w = mg`
`w = 31.81 xx 9.8 = 311.24 N`