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A particle of mass 'm' is projected with...

A particle of mass 'm' is projected with a velocity `upsilon` making an angle of `30^(@)` with the horizontal. The magnitude of angular moment of the projectile about the point of projection when the particle is at its maximum height 'h' is

A

zero

B

`(mv^(2))/(sqrt2g)`

C

`(sqrt3mv^(3))/(16g)`

D

`(sqrt3 mv^(3))/(2g)`

Text Solution

Verified by Experts

The correct Answer is:
C
(c): At highest point, the velocity is only in a-direction and perpendicular distance from the origin of XY-plane is H.

Angular momentum L
`=mv_(x)H`
`=(m v cos 30^(@))H`
`=mv (sqrt3)/(2) ((v^(2) sin ^(2) 30^(@))/(2g))`
`=mu^(3) (sqrt3)/(4g)((1)/(4))`
`L=(sqrt3 mv^(2))/(16g)`
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