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(B) The system consists of two equal rods joined at one end,placed on a smooth horizontal surface. Since the surface is smooth,there is no external ho

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straight vertical line

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(B) The system consists of two equal rods joined at one end,placed on a smooth horizontal surface. Since the surface is smooth,there is no external horizontal force acting on the system. The only external forces acting on the system are the gravitational force (acting downwards) and the normal reaction from the surface (acting upwards). Both these forces act in the vertical direction. According to Newton's second law for the centre of mass,$F_{ext, x} = M a_{cm, x}$. Since there is no external horizontal force $(F_{ext, x} = 0)$,the acceleration of the centre of mass in the horizontal direction is zero $(a_{cm, x} = 0)$. Initially,the system is at rest,so the initial velocity of the centre of mass in the horizontal direction is zero $(v_{cm, x} = 0)$. Since both the initial velocity and acceleration in the horizontal direction are zero,the centre of mass will not move horizontally. Therefore,the centre of mass will move only in the vertical direction. Thus,the trajectory of the centre of mass is a straight vertical line.

Two equal rods joined at one end are kept on a smooth surface as shown and released. The trajectory of the centre of mass of both rods is:

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