A particle is performing U.C.M. along a circle of radius $R$. In half the period of revolution, its displacement and distance covered are respectively

The equation of the trajectory of a ball projected at an angle $\theta$ with the horizontal, is given as $y = x - \dfrac{gx^2}{2}$
The initial velocity of the ball is
[Given : $\tan 45^\circ = 1$, $\cos 45^\circ = \dfrac{1}{\sqrt{2}}$ ]

A stone of mass $40$ g is tied to a light inextensible string of length $50$ cm and whirled in a vertical circle at the rate of $30$ revolutions per minute. The tension in the string when it is at the lowest point of the circle is
(Take gravitational acceleration, $g = 10\,\text{m/s}^2$ and $\pi^2 = 10$)

A body of mass 'm' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is
($g$ = gravitational acceleration)