Two particles A and B are moving as shown in the figure. Their total angular momentum about the point O is

Options

A. `9.8kgm^(2)//s`
B. zero
C. `52.7kgm^(2)//s`
D. `37.9kgm^(2)//s`

Answer

A

Explanation

Total angular momentum of two particles about the point O
`vecL_("net")=vecL_(A)+vecL_(B)=vecr_(A)xxvecP_(A)+vecr_(s)xxvecp_(s)`

Here, `vecr_(A)=1.5mhatj,vecr_(B)=2.8mhati`
`vecP_(A)=mvecv_(A)=(6.5)(2.2hati)=(14.3hati)Ns`
`vecP_(B)=mvecv_(B)=(3.1)(3.6hatj)=(11.16hatj)Ns`
`thereforevecL_("net")=(1.5hatj)xx(14.3hati)+(2.8hati)xx(11.16hatj)`
`=21.45(-hatk)+21.248(hatk)=9.8hatk`
`abs(vecL_("net"))=9.8kgm^(2)s^(-1)`