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A body of mass m= 20 g is attached to an...

A body of mass m= 20 g is attached to an elastic spring of length L=50 cm and spring constant k=2 `Nm^(-1)`. The syste is revolved in a horizontal plan with a frequency v=30 rev/min. Find the radius of the circular motion and the tension in the spring .

A

`0.55 m, 0.1 1N`

B

`0.5 m, 0.52 N`

C

`0.55 m, 0.1 N`

D

`0.9 m, 0.2 N`

Text Solution

Verified by Experts

(c) Angular velocity `omega=2pir=2pixx(30)/(60)=pi rad//s` For an elastic spring force `F=kx.` Where x is the extension
Radius of circular motion `r=L+x`
Centripetal force `=mromega^(2)=F`
`rArr" " M(L+x)omega^(2)=kx`
`rArr" " x=(mLomega^(2))/(k-momega^(2))=(0.02xx0.5xx(3.14)^(2))/(2-0.02xx(3.14)^(2))`
Radius of the circular motion (r) `=L+x=0.5+0.05=0.55 M`
Tension in the spring `T=kx =2xx0.05=0.1 N`
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