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A small particle of mass m is projected at an angle $θ$ with the x-axis with an initial velocity us in the x-y plane as shown in the figure. At a time $t < \frac{v_{0} \sin θ}{g}$ , angular momentum of the particle is :

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12mgv0t2cos⁡θi^

−mgv0t2⋅cos⁡θj^

mgv0tcos⁡θk^

−12mgv0t2cos⁡θk^

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detailed solution

Correct option is D

L→=r→×p→ where r→=xi^+yj^=v0cos⁡θti^+v0sin⁡θt−12gt2j^and p→=mv→=mv0cos⁡θi^+v0sin⁡θ−gtj^So, j→=i^j^ v0cos⁡θtv0sin⁡θt−12gt20mv0cos⁡θmv0sin⁡θ−gt0=−12mgv0t2cos⁡θj^

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A small particle of mass m is projected at an angle θ with the x-axis with an initial velocity us in the x-y plane as shown in the figure. At a time t<v0sin⁡θg, angular momentum of the particle is :

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A small particle of mass m is projected at an angle $θ$ with the x-axis with an initial velocity us in the x-y plane as shown in the figure. At a time $t < \frac{v_{0} \sin θ}{g}$ , angular momentum of the particle is :