A particle of mass `m` is moving along the side of a square of side `a`, with a unifrom speed v in `XY` palne as shown in Fig. Which of the followig statements is false for the angualr momentum `overset rarr(L)` about the origin?

Options

A. `overset rarr(L) = - (mv)/(sqrt(2)) R hatk`, when particle is moving from `A to B`
B. `overset rarr(L) = - (mv)((R )/(sqrt(2))-a) hatk`, when particle is moving from `C to D`
C. `overset rarr(L) = - (mv)((R )/(sqrt(2))+a) hatk`, when particle is moving from `B to C`
D. `overset rarr(L) = - (mv)/(sqrt(2)) R hatk`, when particle is moving from `D to A`

Answer

B, D

Explanation

In option (a), co-ordinates of `A` are `((R )/(sqrt(2)),(R )/(sqrt(2)))`
`:. overset rarr(r ) = ((R )/(sqrt(2))hati +(R )/(sqrt(2))hatj)` and `overset rarr(v) = v hati`
`overset rarr(L)m (overset rarr(r ) xx overset rarr(v)) = m ((R )/(sqrt(2))hati +(R )/(sqrt(2))hatj) xx v hati`
`overset rarr(L) = - (mR)/(sqrt(2)) v hatk`
`:.` Option (a) is correct. Similarly, option (c) is correct. Statements (b) and (d) are false.