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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 `M = 2kg, R = 2m` and `u = 10 m//s`. Then velocity of particle when `theta = 60^(@)` is

A

`2sqrt5m//s`

B

`4sqrt5m//s`

C

`5sqrt2m//s`

D

`5m//s`

Text Solution

Verified by Experts

The correct Answer is:
B
At `theta=60^(@) h=R-R cos 60=R/2`
Put `h=R/2` in `v^(2)-u^(2)=2gh`
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