Two identical balls each of mass M (= 1.25 kg) and radius r are kept in contact and are connected to two identical unstretched springs each of force constant k (= 100 N/m). A third ball also of mass M but radius r/2 strikes with the two balls symmetrically with speed v₀ (= 1.6 m/s) and comes to rest just after the impact. Find the maximum compression in each spring in cm.
Physics · Mixed Chapter
JEE Mains

Question

Two identical balls each of mass M (= 1.25 kg) and radius r are kept in contact and are connected to two identical unstretched springs each of force constant k (= 100 N/m). A third ball also of mass M but radius r/2 strikes with the two balls symmetrically with speed v₀ (= 1.6 m/s) and comes to rest just after the impact. Find the maximum compression in each spring in cm.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The small sphere of radius r/2 hits the two large spheres of radius r symmetrically. At contact the centre separation is 3r/2, the horizontal offset to each large sphere is r, and the vertical offset is √5 r/2. Thus the impact-line horizontal and vertical direction cosines are 2/3 and √5/3. Step 2: When the incoming ball stops, symmetry and vertical momentum give Mv₀=2Mu(√5/3), hence u=3v₀/(2√5). Each large ball's horizontal speed after the collision is u·2/3=v₀/√5. Step 3: At maximum s…