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JEE Mains Question

  • JEE
  • Laws of Motion
  • Centripetal Force
  • 11th

Step-wise Solution

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Question:
If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then to maintain the same centripetal force, the ratio of their velocities will be:

(a) √3 : 2
(b) 1 : √3
(c) √3 : 1
(d) 2 : √3
Quick Solution
Problem Approach

Concept Flashcards

Triangular law of vector addition

It is a graphical method to add two given vectors to find the resultant vector. There are three steps involved in solving the resultant vector. 

  1. Consider any one vector out of two vectors
  2. Place the tail of the second vector to the head of the first vector
  3. Draw the resultant vector from the tail of the first vector to the head of the second vector. 

Uniform Circular Motion

Motion is a change in the position of an object with respect to time. Circular motion means a change in position of an object in a circular path with respect to time. The uniform circular motion means equal change in position of an object in a circular path in equal intervals of time. 

Centripetal force

The force that always acts towards the center when the body moves in a circular path is known as centripetal force. It arises due to the presence of centripetal acceleration. ‘Centri’ means ‘center,’ and ‘petal’ means ‘seeking’ (searching). 

Centripetal force

MCQ challenge

25s

Problem Logical Approach

Step 1

Given data

The masses of two particles are the same. The ratio of the radius of curvature of the two particles is 3:4. If the centripetal forces acting on both the particles are the same, we need to find the ratio of their linear velocities. 

Step 1
Step 2

Equation of Centripetal force

The derivation logic is included in the stepwise solution for your reference. The formula of the centripetal force is mass times the square of linear velocity divided by the radius of the circular path. As per the given data, the centripetal force of the first particle must be equal to the centripetal force of the second particle. 

Step 2
Step 3

Solving for the ratio of linear velocities

Since the masses of both of the particles are the same, they will cancel on both of the sides of the equation. Therefore, the ratio of the velocity of the first particle to the velocity of the second particle must be equal to the square root of the ratio of the linear velocity of the first to the second particle. Substituting the values, velocity ratio is obtained. 

Step 3

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