A solid sphere is pushed on a horizontal surface such that it slides with a speed 3.5 ~ms ⁻¹ initially without rolling. The sphere will start rolling without slipping when its velocity becomes

Step-by-step solution

Solid sphere with velocity, v₁=3.5 ~m / s By conservation of angular momentum aligned & L_i=L_f & m₁ R=I +m₂ R aligned after some time sphere starts pure rolling v ₂= R Moment of inertia of solid sphere, I = 2 5 mR ^2 aligned & mv ₁ R = 2 5 mR ^2 v ₂ R + mv ₂ R & v ₁= 2 5 v ₂+ v ₂ & v ₂= 5 v ₁ 7 = 5 7 3.5=2.5 ~m / s aligned