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# A hollow sphere of radius R rests on a surface of finite coefficient of friction, A point object of mass m moved horizontally and his the sphere at a height of $\large\frac{R}{2}$ above its centre. The collision is completely inelastic. Which of the following is/are correct ? 1) total linear momentum of the system is not conserved 2) total angular momentum about centre of mass of the system remains constant. 3) the sphere gets finite angular velocity immediately after collision. 4) the sphere moves with finite speed immediately after collision.

$a)\; 1,2\; and\; 3 \\b)\; 2,3\; and\; 4 \\ c)\; 1,3 \;and\; 4 \\ d)\; 1,2\;and\; 4$