A particle of mass m is moving along the side of a square of side 'a', with a uniform speed υ…

A particle of mass m is moving along the side of a square of side 'a', with a uniform speed $\mathrm{\upsilon }$ in the x-y plane as shown in the figure:


Which of the following statements is false for the angular momentum $\overrightarrow{\mathrm{L}}$ about the origin?

1. $\overrightarrow{\mathrm{L}}=\mathrm{m}\mathrm{\upsilon }\left[\frac{\mathrm{R}}{\sqrt{2}}+\mathrm{a}\right]\widehat{\mathrm{k}}$
   
   when the particle is moving from B to C.
2. $\overrightarrow{\mathrm{L}}=\frac{\mathrm{m}\mathrm{\upsilon }}{\sqrt{2}}\mathrm{R}\widehat{\mathrm{k}}$
   
   when the particle is moving from D to A.
3. $\overrightarrow{\mathrm{L}}=-\frac{\mathrm{m}\mathrm{\upsilon }}{\sqrt{2}}\mathrm{R}\widehat{\mathrm{k}}$
   
   when the particle is moving from A to B.
4. $\overrightarrow{\mathrm{L}}=\mathrm{m}\mathrm{\upsilon }\left[\frac{\mathrm{R}}{\sqrt{2}}+\mathrm{a}\right]\widehat{\mathrm{k}}$
   
   when the particle is moving from C to D.

Solution

Asked in: JEE Main 2016 (03 Apr)

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