State whether the following statements are true or false:
$(a)$ The value of acceleration due to gravity increases as we go to a depth $d$ below the Earth's surface.
$(b)$ If the escape velocity for an object of mass $m$ on the Earth's surface is $11.2 \, km/s$,then the escape velocity for an object of mass $2m$ is $22.4 \, km/s$.
$(c)$ If the Earth's gravitational attraction suddenly disappears,the mass of an object becomes zero,but its weight remains the same.

(A) False. The acceleration due to gravity at a depth $d$ is given by $g_d = g(1 - d/R)$,which decreases as depth $d$ increases.
$(b)$ False. Escape velocity is given by $v_e = \sqrt{2GM/R}$. It is independent of the mass of the object $m$. Therefore,for an object of mass $2m$,the escape velocity remains $11.2 \, km/s$.
$(c)$ False. Mass is an intrinsic property of an object and remains constant regardless of gravity. Weight is the force of gravity $(W = mg)$,so if gravity disappears,weight becomes zero,but mass remains unchanged.