# A particle of mass m is moving in a circular motion. If the particle increases its radius keeping speed constant, its centripetal force will _________

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A particle of mass m is moving in a circular motion. If the particle increases its radius keeping speed constant, its centripetal force will __________.
1. increase
2. decrease
3. remain constant
4. first increase then decrease

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Correct Answer - Option 2 : decrease

CONCEPT:

• Centripetal Force: The force that makes a body move in a circular motion is known as centripetal force.
• The direction of this force is always perpendicular to the direction of the velocity.

The centripetal force acting on a body of mass 'm' revolving with radius 'r' is:

$F = {mv^2\over r}$

EXPLANATION:

Given that the mass and speed of the particle are constant and radius is changing.

So, The centripetal force on the particle $F = {mv^2\over r}$

$F \propto {1\over r}$

• So as the radius of circular motion increases, the centripetal force on the particle will decrease.
• Hence the correct answer is option 2.