Question

The time period of a spring-mass system is T in air when the mass is partially immersed in water the time period of oscillation is

• A. T
• B. < T
• C. >T
• D. ≤T

Answer 1

Answer: (B)

< T

Answer 2

The time period of the spring mass system in air = T = 2 π $\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$ . When the mass is immersed in water partially, the buoyant force = ρAxg & the spring force = k.x. when the body is displaced through a small distance x. The restoring force = kx + ρAgx

ω′ = $\sqrt { \frac { k + \rho A g } { m } }$

⇒ T′ = 2π$\sqrt { \frac { m } { k + \rho A g } }$

∴ T′ < T

Hence Answer is (B)