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The time dependence of the position of a...

The time dependence of the position of a particle of mass m = 2 is given by `vec(r) (t) = 2t hat(i) - 3 t^(2) hat(j)` Its angular momentum, with respect to the origin, at time t = 2 is :

A

`48(hat(i)+hat(j))`

B

`-34(hat(k)-hat(i))`

C

`-48hat(k)`

D

`36hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(L)=m(vec(r)xxvec(v))`
`{:(vec(v)=2hat(i)-6that(j),impliesvec(v)=2hat(i)-12hat(j), "at" t=2"sec"):}`
`{:(r(t)=2that(i)-3t^(2)hat(j)implies, r(2)=4hat(i)-12hat(j),"at" t=2"sec"):}`
`vec(L)=2|{:(hat(i), hat(j), hat(k)),(4, 12, 0), (2, -12, 0):}|=2(12xx4-12xx2)hat(k)`
`vec(L)=-48hat(k)`
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