One end of a massless spring of spring constant k and natural length \(l_0\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(ω\) about an axis passing through fixed end, then the elongation of the spring will be :
- \(\frac{k-mω^2l_0}{mω^2}\)
- \(\frac{mω^2l_0}{k+mω^2}\)
- \(\frac{mω^2l_0}{k-mω^2}\)
- \(\frac{(k+mω^2l_0)}{mω^2}\)
The Correct Option is C
Solution and Explanation
The elongation of the spring will be :
\(mω^2(l_0 + x) = kx\)
\(⇒ mω^2l_0 = (k – mω^2) × x\)
\(⇒ x=\frac{mω^2l_0}{(k-mω^2)}\)
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Concepts Used:
Friction
Friction is defined as the resistance offered by the surfaces that are in contact when they move past each other.
Types of Friction
There are four categories of Friction- static friction, sliding friction, rolling friction, and fluid friction.
Sliding Friction
In Sliding Friction, the weight of the sliding object calculates the amount of sliding friction present between the two objects. The sliding friction is supposed to be greater as the pressure exerted by the heavy object on the surface it slides over is comparably more.
Rolling Friction
Friction between a circular object and the surface is called as Rolling Friction. It is required to overcome sliding friction is more than the force required to overcome the rolling friction.
Static Friction
Friction that keeps an object at rest without initiating any relative motion between the body and the surface is termed as Static Friction. For example, a parked car resting on the hill, a hanging towel on the rack. The maximum force of static friction is directly proportional to the normal force.
Fluid Friction
Fluid Friction is the kind of friction that is exerted by the fluid on the object that is moving through a fluid.