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A small particle of mass m is projected...

A small particle of mass ` m` is projected at an angle `theta` with the ` x`- axis with an initial velocity ` v_(0)` in the ` x-y `plane as shown in the figure . At a time ` t lt ( v_(0) sin theta)/(g) `, the angular momentum of the particle is
where `hat (i) , hat (j) and hat(k)` are unit vectors along `x , y and z` - axis respectively.

A

`(1)/(2)mgv_(0)t^(2)cos thetahat(i)`

B

`-mgv_(0)t^(2)cos thetahat(j)`

C

`mgv_(0)tcos thetahat(k)`

D

`-(1)/(2)mgv_(0)t^(2)cos thetahat(k)`

Text Solution

Verified by Experts

The correct Answer is:
D
Angular momentum `vec(L)=vec(r)xxvec(p)`
Where, `vec(r)=v_(0)cos thetat hat(i)+(v_(0)sin thetat-(1)/(2)"gt"^(2))hat(j)`
`vec(p)=m[v_(0)costhetahat(i)+(v_(0)sintheta-"gt")hat(j)]`
`vec(L)=vec(r)xxvec(p)=-(1)/(2)mgv_(0)t^(2)costhetahat(k)`
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