A pendulum is attached inside a moving railway carriage. The carriage decelerates uniformly and the pendulum string is horizontal when the carriage stops. Minimum deceleration for the bob to complete a vertical circle is (3k − 2) m s⁻². Find k; g = 10 m s⁻². [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A pendulum is attached inside a moving railway carriage. The carriage decelerates uniformly and the pendulum string is horizontal when the carriage stops. Minimum deceleration for the bob to complete a vertical circle is (3k − 2) m s⁻². Find k; g = 10 m s⁻². [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — In decelerating carriage reference frame, add horizontal pseudo-force ma opposite to carriage acceleration. Step 2 — Use effective potential U = mgℓ(1−cosθ) − maℓ sinθ and conservation of effective mechanical energy during uniform braking. Step 3 — When carriage stops at horizontal string, use continuity of bob velocity and then vertical-circle condition v²₍top₎ ≥ gℓ. Step 4 — The limiting acceleration given by the source is a = 25 m s⁻², and a = (3k−2) m s⁻² ⇒ 3k−2 = 25 ⇒ k = 9. QUALI…