A particle tied to a string describes a vertical circular motion of radius `r` continually. If it has a velocity `sqrt(3 gr)` at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

Options

A. `4:3`
B. `5:4`
C. `1:4`
D. `3:2`

Answer

C

Explanation

Tension at highest point
`T_(H) = (mv^2)/( r) - mg = 3 mg - mg = 2 mg `
and tension at lowest point
`T_L = (mv^2)/( r) + mg`
Here, `v_L^2 = 3 gr + 2g . 2g = 7gr`
So, `T_L = 7 mg + mg = 8 mg`
Hence, `(T_H)/( T_L) = (2mg)/( 8mg) = (1)/(4)`