Question

A body of mass 4 kg is moving in a circle of radius 1m with an angular velocity of 2 radian/sec.  Find Centripetal Force acting on the body.

1. 8N
2. 20N
3. 16N
4. 24N

Answer 1

Correct Answer - Option 3 : 16N

Concept:

Centripetal Force: 

• The force that makes a body to 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' and constant speed v is given as

\(F = {mv^2\over r}\)

Angular Velocity:

• The rate of angular displacement by an object is called angular velocity.
• It is represented by ω.
• It is represented as a division of speed by radius at a particular point.

\(ω = \frac{v}{r}\)

• The Centripetal force in term of angular velocity is represented as

F = m ω ² r

Calculation:

Given mass of the body = 4kg

Angular velocity ω = 2 radian / sec

radius r = 1m

Force F = 4 kg × (2 radian/sec)² × 1m 

⇒ F = 16 N

So, the correct option is 16 N.

 

• Angular velocity might get confused with speed. Questions should be read carefully.