An inextensible string connects block A, pulled right from rest position with constant horizontal speed u = 1 m s⁻¹, to block B on 30° incline via pulley P at end of 12 m incline. Initially A is 2 m high as shown. If time for B to reach P is k√15 seconds, find k. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

An inextensible string connects block A, pulled right from rest position with constant horizontal speed u = 1 m s⁻¹, to block B on 30° incline via pulley P at end of 12 m incline. Initially A is 2 m high as shown. If time for B to reach P is k√15 seconds, find k. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Total rope length remains fixed: length from moving A to pulley plus length along incline from B to pulley is constant. Step 2 — Let s be rope segment A–P length. Horizontal block A displacement u t alters s by the Pythagorean distance to elevated pulley. Step 3 — B reaches pulley when decrease in its segment equals its initial slant distance 12 m; use pulley height 2 m and 30° incline from image. Step 4 — Solve geometric relation for time t and compare with t = k√15 s. Printed k = 4.…