In the adjacent figure, three identical small spheres A, B and C each of mass m are lying at rest on a smooth horizontal surface. Spheres A & B, B & C are connected by light and inextensible strings. The strings are just taut when angle between AB and BC, ∠ABC = 120°. The sphere B is given an impulse J along x-axis. If the initial speed acquired by the sphere A just after giving impulse J is equal to kJ/(3m), find the value of k.
Physics · Mixed Chapter
JEE Mains

Question

In the adjacent figure, three identical small spheres A, B and C each of mass m are lying at rest on a smooth horizontal surface. Spheres A & B, B & C are connected by light and inextensible strings. The strings are just taut when angle between AB and BC, ∠ABC = 120°. The sphere B is given an impulse J along x-axis. If the initial speed acquired by the sphere A just after giving impulse J is equal to kJ/(3m), find the value of k.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The configuration is symmetric about the x-axis. Therefore immediately after the impulse, B moves along x, while A and C move symmetrically along the taut strings. Step 2: With each string making 60° with the negative x direction, the speed of A (or C) along the string is v_A = v_B cos60° = v_B/2. Step 3: Conserve horizontal momentum: J=mv_B+2mv_A cos60°=mv_B+mv_A=3mv_A. Step 4: Hence v_A=J/(3m) and k=1.