A small ball of mass m is connected by an inextensible massless string of length l with another ball of mass M = 4m. They are released with zero tension in the string from a height h as shown in the figure. The string becomes taut for the first time after the mass M collides with the ground (assume all collisions to be elastic), after a time l/√(ngh), where n = _____.
Physics · Mixed Chapter
JEE Mains

Question

A small ball of mass m is connected by an inextensible massless string of length l with another ball of mass M = 4m. They are released with zero tension in the string from a height h as shown in the figure. The string becomes taut for the first time after the mass M collides with the ground (assume all collisions to be elastic), after a time l/√(ngh), where n = _____.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Both balls initially fall with g, so their separation remains l and the string has zero tension. The lower ball M hits the ground with speed v=√(2gh). Step 2: After elastic bounce, M moves upwards at v while the upper ball m continues downwards at v. Their relative speed just after the collision is 2v. Both have the same downward gravitational acceleration, so their relative speed remains constant until tension returns. Step 3: They first move towards one another by separation l, cross,…