Question:
A stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making n rev/min. The total tension in the string when the stone is at the lowest point is
A stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making n rev/min. The total tension in the string when the stone is at the lowest point is
Updated On: Jul 6, 2022
- mg
- $m(g + \pi nr^2)$
- m(g + nr)
- $m\begin{Bmatrix}g+\frac{\pi^2n^2r}{900}\end{Bmatrix}$
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The Correct Option is D
Solution and Explanation
$T_{net} = \frac{m\nu^2}{r} + mg = mr\omega^2 + mg$
= $mr\left(\frac{2\pi n }{60}\right)^2 +mg$
= $m \left[\frac{\pi^2n^2r}{900} + g\right]$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration