Physics Rotational & Circular Motion PMDC 2020
PMDC Verified Question 75 of 95
If during circular motion, tangential velocity of a body becomes double, then centripetal force becomes:
A
Double
B
One half
C
Four times
D
One fourth
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: Four times
Concept:

Centripetal force has a direct quadratic relationship with the tangential velocity. Any change in velocity causes a squared effect on the required force.

Formula:

$$ F_c = \frac{mv^2}{r} $$

Solution:

  • Let initial force be \( F = \frac{mv^2}{r} \).
  • If velocity is doubled, new velocity is \( 2v \).
  • Substitute \( 2v \) into the formula: \( F' = \frac{m(2v)^2}{r} = \frac{m(4v^2)}{r} \).
  • Pulling the 4 out, we get \( F' = 4 \left( \frac{mv^2}{r} \right) = 4F \).
  • Therefore, the force becomes four times as great.


Why other options are incorrect:

  • Option A assumes a linear relationship rather than a squared one.
  • Option B and Option D assume an inverse relationship.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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