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Question:

A small particle of mass m is projected at an angle θ with the x-axis with an initial velocity v₀ in the xy-plane as shown in the figure. At a time t < v₀sinθ/g, the angular momentum of the particle is: (here ^i, ^j, and ^k are unit vectors along x, y, and z-axis respectively)

mgv₀tcosθ^k

−mgv₀t²cosθ^j

½mgv₀t²cosθ^k

12mgv₀t²cosθ^i

Solution:

→L=m(→r×→v)
→L=m[v₀cosθt^i+(v₀sinθt−½gt²)^j]×[v₀cosθ^i+(v₀sinθ−gt)^j]=mv₀cosθt[−½gt]^k=½mgv₀t²cosθ^k