A stone tied to a string is rotated with a uniform speed in a vertical plane. If mass of the stone is `m`, the length of the string is `r` and linear speed of the stone is `v` when the stone is at its lowest point, then the tension in the string will be
(g= acceleration due to gravity)

Options

A. `mg`
B. `(mv^(2))/(r)-mg`
C. `(mv)/(r)`
D. `(mv^(2))/(r)+mg`

Answer

D

Explanation

For a stone of mass `m` and length of string `r` at the point `B` , weight `mg` acts vertically downwards, while tension `T_(B)` acts vertically upward. Their resultant provides the necessery centripetal force, that is
`T_(B)-mg=(mv^(2))/(r)`
implies `T_(B)=(mv^(2))/(r)+mg`
This is the tension of string at lowest point.