Question:

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A) : A ball connected to a string is in circular motion on a frictionless horizontal table and is in equilibrium. 

Reason (R): Magnitude of the centripetal force is equal to the magnitude of the tension in the string. 

In the light of the above statements, choose the correct answer from the options given below
 

Updated On: May 8, 2024
  • Both (A) and (R) are true and (R) is the correct explanation of .
  • Both (A) and (R) are true but (R) is not the correct explanation of .
  • (A) is true but (R) is not true.
  • (A) is not true but (R) is true.
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The Correct Option is B

Solution and Explanation

In a circular motion, the direction of resultant force is towards centre and its magnitude is $ F=\frac{m{{v}^{2}}}{r} $ or $ F=mr{{\omega }^{2}} $ Thus, a centripetal force of magnitude $ \frac{m{{v}^{2}}}{r} $ is needed to keep the particle moving in a circle with constant speed.
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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