The body of mass 100 gm is suspended on a weightless spring of stiffness 500 N/m and natural length of 100 cm. Then the body is spun with a frequency of 5 Hz so that the spring describes a cone in spa

Question

The body of mass 100 gm is suspended on a weightless spring of stiffness 500 N/m and natural length of 100 cm. Then the body is spun with a frequency of 5 Hz so that the spring describes a cone in space (Fig). Determine extension in the spring (in cm). Take : π 2 = 10

TestHub · Accepted Answer

The horizontal spring force provides centripetal force.

$k x sin θ = m ω^{2} (ℓ_{0} + x) sin θ$

$ω = 2 π f = 10 π rad/s$

$500 x = (0.1) (100 π^{2}) (1 + x)$

$500 x = 100 (1 + x)$

$\Rightarrow x = 0.25 m$

$x = 25 cm$

Physics - Circular Motion Question with Solution | TestHub

Doubts & Discussion