A 2 kg mass is suspended by a rubber cord 2 m long and of cross-section 0.5 cm. It is made to describe a horizontal circle of radius 50cm in 4 times a second. Find the extension of the cord.(Young's modulus `Y=7xx10^(8) Nm^(-2)`)

Explanation

Given, m=2kg, `omega=2pif=2pixx4=8pi "rads"^(-1),r=0.5` m

From the figure,
`T=" cos"theta=mg` and `T" sin"theta=(mv^(2))/(r)=momega^(2)`
Tension in cord
`T=sqrt((T" sin"theta)^(2)+(T" cos"theta)^(2))`
`=sqrt((momega^(2)r)^(2)+(mg)^(2))`
`T=sqrt([2xx(8pi)^(2)xx0.5]^(2)+[2xx10]^(2))=631 N`
The extension of cord,
`DeltaL=(TL)/(AY)=(631xx2)/(0.5xx10^(-4)xx10^(8))`
`=360xx10^(-4)m=3.60cm`