A particle of mass M attached to an inex...

A particle of mass `M` attached to an inextensible strintg is moving in a vertical circle of radius `R`.about fixed point `O`. It is imparted a velocity `u` in horizontal directional at lowest position as shown in figure.
Following information is being given
(i) Velocity at a height `h` can be calculated by using formula `v^(2)=u^(2)-2gh`
(ii) Particle will complete the circle if `u ge sqrt(5gR)`
(iii) Particle will oscillates in lower half `(0^(@)ltthetale90^(@))` if `0ltu lesqrt(2gR)`
(iv) The magnitude of tension at a height `'h'` is calculated by using formula `T=M/R[u^(2)+[gR-3gh]]`

If `R = 2m, M = 2 kg` and `u = 12 m//s`. Then value of tension at lowest position is

`120 N`

`164 N`

`264 N`

zero

Verified by Experts

The correct Answer is:

Put `h=0 T=164N`

A particle of mass M attached to an inextensible strintg is moving in a vertical circle of radius R .about fixed point O . It is imparted a velocity u in horizontal directional at lowest position as shown in figure. Following information is being given (i) Velocity at a height h can be calculated by using formula v^(2)=u^(2)-2gh (ii) Particle will complete the circle if u ge sqrt(5gR) (iii) Particle will oscillates in lower half (0^(@)ltthetale90^(@)) if 0ltu lesqrt(2gR) (iv) The magnitude of tension at a height 'h' is calculated by using formula T=M/R[u^(2)+[gR-3gh]] If M = 2kg, R = 2m and u = 10 m//s . Then velocity of particle when theta = 60^(@) is

`2sqrt5m//s`

`4sqrt5m//s`

`5sqrt2m//s`

`5m//s`

`100 N`

`44 N`

`144 N`

`264 N`

` (3mv_(0)^(2))/(r)`

`(9 mv_(0)^(2))/(r)`

3mg

both (A) and (C) are correct