Two particles A and B of equal masses m each are connected by a string of length 1 m and lie on a smooth horizontal plane. Gravity is acting perpendicular to the plane of paper inwards. The particle B is given an initial velocity of 5 m/s perpendicular to the string as shown in the figure. Find the initial radius of curvature of path followed by the particle B (in metres).
Physics · Mixed Chapter
JEE Mains

Question

Two particles A and B of equal masses m each are connected by a string of length 1 m and lie on a smooth horizontal plane. Gravity is acting perpendicular to the plane of paper inwards. The particle B is given an initial velocity of 5 m/s perpendicular to the string as shown in the figure. Find the initial radius of curvature of path followed by the particle B (in metres).

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Immediately after the transverse impulse, the equal masses have no external force in the tabletop plane; string tension accelerates B inward and A toward B. Step 2: The separation remains fixed, and their relative transverse speed is v=5 m/s. Its radial acceleration is v²/L. For equal masses, the inward acceleration of each particle from the tension is v²/(2L). Step 3: The initial trajectory curvature of B satisfies v²/R꜀=v²/(2L), hence R꜀=2L=2 m. Answer: 2.