A uniform disc of radius R rolls without sliding on a horizontal surface. The velocity of centre of mass of the disc is V. Att = 0, the point of contact (P) of the edge of the disc is at origin. Take the fixed horizontal surface as X-axis. Now find (a) the co-ordinates of Pas function of time. (b) nature of path traced by P.(c) velocity of P. (d) distance covered by P during one period of rotation relative to the fixed surface.

A uniform disc of radius R rolls without sliding on a horizontal surfa

1.	A uniform disc of radius R rolls without sliding on a horizontal surface. The velocity of centre of mass of the disc is V. Att = 0, the point of contact (P) of the edge of the disc is at origin. Take the fixed horizontal surface as X-axis. Now find (a) the co-ordinates of Pas function of time. (b) nature of path traced by P.(c) velocity of P. (d) distance covered by P during one period of rotation relative to the fixed surface.
Answer» Solution :(a)X=(Vt-R SIN`theta`),y=R(I-cos `theta`),(b)cycloid ,(C )`V_(P)=2Vsin (theta)/(2)`,(d)8R