A solid right circular cylinder of weight 10 kg and cross sectional area `100cm^2` is suspended by a spring, where `k=1(kg)/(cm)`, and hangs partially submerged in water of density `1000(kg)/(m^3)` as shown in Fig. What is its perod when it makes simple harmonic vertical oscillations? (Take `g=10(m)/(s^2)`)

Options

A. 0.6 s
B. 1 s
C. 1.5 s
D. 2.2 s

Answer

A

Explanation

Let the cylinder by depressed a distance x metres into water from the position of rest.
Increase in tension of spring `=100x` metres into water from the position of rest
Increase in tension of spring`=100xkg-wt`
`(A=100cm^2=10^-2m^2)`
Increase in buoyancy `=(100)/(100^2)x xx1000kg-wt`
`K=1(kg-wt)/(cm)=100(kg-wt)/(m)=10xkg-wt`
Total unbalanced vertical force on the cylinder
`=100x+10x=110xkg-wt`
Acceleration of cylinder`=(110x xx10)/(10)(m)/(s^2)=110x(m)/(s^2)`
Period of one oscillation`=(2pi)/(sqrt(110))=0.6s`