A uniform solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling. Then the value of h and speed of centre of mass are

Question

A uniform solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling. Then the value of h and speed of centre of mass are, h = 2 5 R and v = J M, h = 2 5 R and v = 2 5 J M, h = 7 5 R and v = 7 5 J M, h = 7 5 R and v = J M

MARKS App · Accepted Answer

Let the force producing impulse J is F . ⇒ F × h = 2 5 m R 2 × a Also, F = m a (where a = R α ) ∴ m a h = 2 5 m R a ⇒ h = 2 5 R Also impulse = change in momentum or, J = M v ⇒ v = J M

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