A solid right circular cylinder of weight $$10$$ kg and $$cross-$$ section al area $$100$$ $$cm2$$ is suspended by a spring, where $$k=11$$ $$kg/cm$$, and hangs partially submerged in water of density $$1000$$ $$kg/m3$$ as shown in figure. What is its period when it makes simple harmonic vertical oscillations? (Take$$ $$g=10$$ $$m/s2)

Question

Infinity Learn · Accepted Answer

Let the cylinder be depressed a distance x metres into waterfrom the position of rest.Increase in tension of spring $$=$$ $$100x$$ metres into water fromthe position of restIncrease in tension of spring $$=$$ $$100x$$ $$kg-wtA=100cm2=10$$−$$2m2$$ Increase in buoyancy $$=1001002x$$×$$1000kg$$−wtK $$=$$ $$1$$ $$kg-wt/cm$$ $$=$$ $$100$$ $$kg-wt/m$$ $$=$$ $$10x$$ $$kg-wtTotal$$ unbalanced vertical force on the $$cylinder=100x+$$ $$10x=$$ $$110x$$ $$kg-wt$$ Acceleration of cylinder $$=110x$$×$$1010m/s2=110xm/s2$$ Period of one oscillation $$=2$$$$π$$$$110=0.6s$$

A solid right circular cylinder of weight 10 kg and cross- section al area 100 cm² is suspended by a spring, where k=11 kg/cm, and hangs partially submerged in water of density 1000 kg/m³ as shown in figure. What is its period when it makes simple harmonic vertical oscillations? (Take g=10 m/s²)

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A solid right circular cylinder of weight 10 kg and cross- section al area 100 cm2 is suspended by a spring, where k=11 kg/cm, and hangs partially submerged in water of density 1000 kg/m3 as shown in figure. What is its period when it makes simple harmonic vertical oscillations? (Take g=10 m/s2)

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A solid right circular cylinder of weight 10 kg and cross- section al area 100 cm² is suspended by a spring, where k=11 kg/cm, and hangs partially submerged in water of density 1000 kg/m³ as shown in figure. What is its period when it makes simple harmonic vertical oscillations? (Take g=10 m/s²)