A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v_0 in the x-y plane. At a time t < v_0 θ/g , the angular momentum of the particle about the origin is: ![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/d1d8dfb8-c622-4506-801a-a60435bf

Angular momentum L = r × p = m(r × v) . r = (v_0 θ t)i + (v_0 θ t - 1/2gt^2)j v = (v_0 θ)i + (v_0 θ - gt)j r × v = [(v_0 θ t)(v_0 θ - gt) - (v_0 θ t - 1/2gt^2)(v_0 θ)]k r × v = [v_0^2 θ θ t - v_0 θ gt^2 - v_0^2 θ θ t + 1/2v_0 θ gt^2]k r × v = -1/2 g v_0 t^2 θ k L = -1/2 m g v_0 t^2 θ k .

A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v_0 in the x-y plane. At a time t < v_0 θ/g , the angu - Physics MCQ AIEEE 2026 | ExamTest.live

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A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v_{0} in the x - y plane. At a time t < \frac{v _{0} s i n θ}{g}, the angular momentum of the particle about the origin is:

A $- m g v_{0} t^{2} cos θ \hat{j}$
B $m g v_{0} t cos θ \hat{k}$
C $- \frac{1}{2} m g v_{0} t^{2} cos θ \hat{k}$
D $\frac{1}{2} m g v_{0} t^{2} cos θ \hat{i}$

Solution & Step-by-step Explanation

Angular momentum L = r \times p = m (r \times v) . r = (v_{0} cos θt) \hat{i} + (v_{0} sin θt - \frac{1}{2} g t^{2}) \hat{j} v = (v_{0} cos θ) \hat{i} + (v_{0} sin θ - g t) \hat{j} r \times v = [(v_{0} cos θt) (v_{0} sin θ - g t) - (v_{0} sin θt - \frac{1}{2} g t^{2}) (v_{0} cos θ)] \hat{k} r \times v = [v_{0}^{2} sin θ cos θt - v_{0} cos θ g t^{2} - v_{0}^{2} sin θ cos θt + \frac{1}{2} v_{0} cos θ g t^{2}] \hat{k} r \times v = - \frac{1}{2} g v_{0} t^{2} cos θ \hat{k} L = - \frac{1}{2} m g v_{0} t^{2} cos θ \hat{k} .

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A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v_{0} in the x - y plane. At a time t < \frac{v _{0} s i n θ}{g}, the angular momentum of the particle about the origin is:

- m g v_{0} t^{2} cos θ \hat{j}

m g v_{0} t cos θ \hat{k}

- \frac{1}{2} m g v_{0} t^{2} cos θ \hat{k}

\frac{1}{2} m g v_{0} t^{2} cos θ \hat{i}

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A small particle of mass $m$ is projected at an angle $θ$ with the $x$ -axis with an initial velocity $v_{0}$ in the $x - y$ plane. At a time $t < \frac{v _{0} s i n θ}{g}$ , the angular momentum of the particle about the origin is:

Solution & Step-by-step Explanation

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A small particle of mass m is projected at an angle θ with the x -axis with an initial velocity v0​ in the x−y plane. At a time t<gv0​sinθ​, the angular momentum of the particle about the origin is:

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Discussion

A small particle of mass $m$ is projected at an angle $θ$ with the $x$ -axis with an initial velocity $v_{0}$ in the $x - y$ plane. At a time $t < \frac{v _{0} s i n θ}{g}$ , the angular momentum of the particle about the origin is: