Two particles of same mass are moving in the circular paths r1 and r2 radius with same speed, the ratio of their centripetal forces is :

  1. \(\sqrt{r_2} : \sqrt{r_1}\)
  2. \(\sqrt{r_1} : \sqrt{r_2}\)
  3. \(r_1 : r_2\)
  4. \(r_2 : r_1\)

Answer (Detailed Solution Below)

Option 4 : \(r_2 : r_1\)
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Detailed Solution

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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' is:

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

CALCULATION:

Given that mass and velocity of both bodies is the same.

So, The centripetal force on the first body \(F_1 = {mv^2\over r_1}\)

The centripetal force on the second body \(F_2 = {mv^2\over r_2}\)

\(F_1 : F_2 =r_2 : r_1\)

So the correct answer is option 4.

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