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A body of mass 100 gram is tied to one end of the spring of length 4 m and whirled in a horizontal circle. Find the maximum frequency with which the body can be whirled if the spring breaks under a tension of 45 kg wt.

A body of mass 100 gram is tied to one end of the spring of length 4 m and whirled
in a horizontal circle. Find the maximum frequency with which the body can be whirled
if the spring breaks under a tension of 45 kg wt.

Grade:12

1 Answers

Kapil Khare
80 Points
5 years ago
Let the maximum frequency with which the body can be whirled be f.
 
 
Maximum tension that spring can bear = (45 * 9.8)N = 441 N
\implies Maximum centripetal force that can be act on mass using this spring = 441N
Angular velocity of the mass = \omega = 2*\pi*f
 
Centripetal force = m\omega2r
\implies                F = (100/1000) * (2*\pi*f)2 * 4
\implies            441 = 16*f2                                           (taking \pi2 = 10)
\implies                f = (441/16)^(1/2)
\implies                f = 21/4 Hz
\implies                f = 5.25 Hz

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