Rotational Motion

JEE Main level, single correct, medium

227 of 280

Question 227 of 280

A particle of mass m is moving along the side of a square of side 'a', with a uniform speed υυ in the x-y plane as shown in the figure:


Which of the following statements is false for the angular momentum L⃗\vec{L} about the origin?

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Answer: (B) L⃗=mυ2Rk^\vec{L}=\dfrac{mυ}{\sqrt{2}}R\hat{k}

when the particle is moving from D to A.

L⃗=r⃗×P⃗\vec{L}=\vec{r}\times \vec{P} or L⃗=rpsin⁡⁡θn^\vec{L}=rp\sin ⁡\theta \hat{n}

For D to A, L⃗=R2mv(−k^)\vec{L}=\dfrac{R}{\sqrt{2}}mv\left(-\hat{k}\right)

For A to B, L⃗=R2mv(−k^)\vec{L}=\dfrac{R}{\sqrt{2}}mv\left(-\hat{k}\right)

For C to D, L⃗=(R2+a)mv(k^)\vec{L}=\left(\dfrac{R}{\sqrt{2}}+a\right)mv\left(\hat{k}\right)

For B to C, L⃗=(R2+a)mv(k^)\vec{L}=\left(\dfrac{R}{\sqrt{2}}+a\right)mv\left(\hat{k}\right)

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