(B) Let $x$ be the extension in the spring. The total length of the spring becomes $r = l + x$.The centripetal force required for the circular motion

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$\frac{m\omega^2 l}{k - m\omega^2}$

(B) Let $x$ be the extension in the spring. The total length of the spring becomes $r = l + x$.The centripetal force required for the circular motion of mass $m$ is provided by the spring force.$F_{\text{spring}} = F_{\text{centripetal}}$$k x = m \omega^2 r$Substituting $r = l + x$:$k x = m \omega^2 (l + x)$$k x = m \omega^2 l + m \omega^2 x$$k x - m \omega^2 x = m \omega^2 l$$x (k - m \omega^2) = m \omega^2 l$$x = \frac{m \omega^2 l}{k - m \omega^2}$

Class 11 Physics 3-2.Motion in Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

Medium

$A$ mass $m$ is attached to one end of a spring with spring constant $k$ and natural length $l$. The system is rotated in a horizontal plane with an angular velocity $\omega$. What is the extension in the length of the spring?

A
$\frac{m\omega^2 l}{k}$
B
$\frac{m\omega^2 l}{k - m\omega^2}$
C
$\frac{m\omega^2 l}{k + m\omega^2}$
D
None of these

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3-2.Motion in Plane

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ mass $m$ is attached to one end of a spring with spring constant $k$ and natural length $l$. The system is rotated in a horizontal plane with an angular velocity $\omega$. What is the extension in the length of the spring?

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$A$ vehicle is moving on a track with constant speed as shown in the figure. The apparent weight of the vehicle is:

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$Assertion$ : Centripetal and centrifugal forces cancel each other.$Reason$ : Centrifugal force is a reaction of centripetal force.

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$Assertion$ : Centripetal and centrifugal forces cancel each other.
$Reason$ : Centrifugal force is a reaction of centripetal force.