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

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)

Two stones of masses $m$ and $3m$ are whirled in horizontal circles, the heavier one in a radius $\dfrac{r}{3}$ and the lighter one in radius $r$. When both the stones experience same centripetal forces, the tangential speed of lighter stone is '$n$' times that of the value of heavier stone. The value of '$n$' is