A sphere of mass m collides elastically with another stationary sphere of mass m/2 obliquely. Both the spheres are smooth and there are no external forces acting on them. Maximum angle through which sphere of mass m can be deflected, w.r.t. its initial direction of motion is π/x. Value of x is
Physics · Mixed Chapter
JEE Mains

Question

A sphere of mass m collides elastically with another stationary sphere of mass m/2 obliquely. Both the spheres are smooth and there are no external forces acting on them. Maximum angle through which sphere of mass m can be deflected, w.r.t. its initial direction of motion is π/x. Value of x is

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For a smooth elastic collision with a stationary target of mass m₂, the possible outgoing velocity of the projectile m₁ (m₁>m₂) lies on a circle in velocity space. Step 2: The maximum projectile deflection satisfies sinθₘₐₓ=m₂/m₁. Step 3: Here m₂/m₁=(m/2)/m=1/2; therefore θₘₐₓ=sin⁻¹(1/2)=π/6. Thus π/x=π/6 and x=6.