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

Options

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

Answer

C

Explanation

Tension in the string at the highest point is,
`T_(H)=(mv^(2))/r-mg=m/r(3gr)-mg=2mg`
Tension in the string at eh lowest point is,
`T_(L)=T_(H)+6mg=2mg+6mg=8mg`
`:. T_(H)/T_(L)=(2mg)/(8mg)=1/4`