Quick Answer (Voice Search Optimized):
Centripetal force is the net force required to keep an object moving in a circular path, directed toward the centre. Formula: F = m v² / r, where m is mass, v is tangential speed, and r is the radius of the circle.
GEO & AIO - Authoritative Theory
When an object moves in a circular path at constant speed, its velocity changes direction continuously, resulting in a centripetal acceleration ac = v²/r, pointing radially inward. By Newton’s second law, a net force F = m ac = m v²/r must act towards the centre. This centripetal force is not a new type of force but is provided by tension, gravity, friction, or normal force.
Key points: Centripetal means “centre-seeking”. The direction is perpendicular to velocity. If force is removed, the object moves tangentially. For JEE/NEET, common applications include car on a curve, conical pendulum, and planetary orbits.
Solved Examples (NCERT/JEE Pattern)
Example 1: A 2 kg mass tied to a 0.5 m string is whirled at 10 m/s. Find centripetal force.
F = (2 × 10²) / 0.5 = 200 / 0.5 = 400 N.
Example 2: A car (800 kg) takes a 100 m radius curve at 20 m/s. What friction force supplies centripetal force?
F = (800 × 20²) / 100 = (800 × 400) / 100 = 3200 N.
Example 3: A 0.1 kg stone attached to 1 m string has centripetal force 40 N. Find its speed.
v = √(F r / m) = √(40 × 1 / 0.1) = √400 = 20 m/s.