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

Two particles having mass 'M' and 'm' are moving in a circular path with radius 'R' and 'r' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to that of the second particle will be