A particle is moving in a vertical circle with constant speed. The tensions in the string when passing through two positions at angles `30^@` and `60^@` from vertical (lowest position) are `T_1` and `T_2` respectively. Then

Options

A. `T_(1)=T_(2)`
B. `T_(2)gtT_(1)`
C. `T_(1)gtT_(2)`
D. Data insufficient

Answer

C

Explanation

Tension, `T=(mv^(2))/(r)+mg costheta`
For `theta=30^(@)`
`T_(1)=(mv_(1)^(2))/(r)+"mg cos 30"^(@)`
For `theta=60^(@),T_(2)=(mv_(2)^(2))/(r)+"mg cos 60"^(@)`
`therefore" "T_(1)gtT_(2)" as "v_(1)gtv_(2)` and `cos30^(@)gtcos60^(@)`