Question

AN OBJECT IS MOVING ALONG THE CIRCUMFERENCE OF A CIRCULAR TRACK. OF RADIUS (R).WHAT IS THE DISPLACEMENT OF THE OBJECT WHEN IT COVERS 3/4 OF ITS CIRCUMFERENCE.

Answer 1

Consider a circle of radius $R$ and suppose that the object starts from $(R,0)$ and moves on the circle counter clockwise. It reaches the point $(0,-R)$ exactly after covering $3/4$th of circumference. So the displacement is given by the distance between starting and final positions : 
displacement = $\sqrt{(0-R)^2+(-R-0)^2}=R\sqrt{2}$