A unit mass at position vector `vecr=(3hati+hatj)` is moving with velocity `vecv=(5hati-6hatj)`. What is the angular momentum of the body about the origin?

Options

A. `0 and 8hati+8hatkN-m`
B. `0 and 4hati+4hatkN-m`
C. `0 and 2hati+2hatkN-m`
D. None of these

Answer

A

Explanation

Given, mass, m = 0.25 kg, `r=2hati-2hatkm`
`v=-5hati+5hatkms^(-1), F=4hatjN`
L and `tau=?`
Angular momentum, `L=r xxp =r xx mv=m(rxxv)`
Now`" "rxxv=|(I,j,k),(2,0,-2),(-5,0,5)|`
`=hati[(0xx5)-(0xx-2)]-hatj[(2xx5)-(-2 xx-5)]+hatk[2xx0-(0xx-5)]=0`
So, angular momentum of particle is zero.
and `tau` = torque `=rxxF=|(hati,hatj,hatk),(2,0,-2),(0,4,0)|=8hati+8hatkN-m`