A particle of mass 1 kg moving in a vertical circular path of radius 1m. Difference of maximum & minimum tension is 60 N. Now if the particle moves with double the velocity of previous lowest position then difference of maximum and minmum tension is.

Options

A. 10 N
B. 30 N
C. 60 N
D. 90 N

Answer

C

Explanation

`T - mg = (m u^(2))/(l)`
`T_("max") = mg + (m u^(2))/(l)` … (1)
`T + mg = (mv^(2))/(l)`
`T_("min") = (mv^(2))/(l) - mg` …(2)
Also, applying WET,
`- mg(2 l) = (1)/(2) mv^(2) - (1)/(2) m u^(2)`
`v^(2) = u^(2) - 4gl` ...(3)
from (1), (2) and (3),
`T_("max") - T_("min") = (mg + (m u^(2))/(l))`
`- [m ((u^(2) - 4gl))/(l) - mg]`
`T_("max") - T_("min") = 6 mg`
which is independent of u.