The unit mass having `r = 8 hat(i) - 4 hat(j) and v = 8 hat(i) + 4 hat(j)` in its angular momentum is

Options

A. 64 units in `-hat(k)` direction
B. 64 units in `+hat(k)` direction
C. 64 units in `+ hat(j)` direction
D. 64 units in `+ hat(i)` direction

Answer

B

Explanation

For a body of mass `m` rotating with velocity `v` in a circle of radius r, then angular momentum is given by
`L = m(r xx v)`
For unit mass, `m=1`
`:. |L|=[(8 hat(i)-4hat(j))xx(8hat(i)+4hat(j))]`
` rArrL=|{:(hat(i),hat(j),hat(k)),(8,-4,0),(8,4,0):}|`
`rArr L=hat(i)(0-0)-hat(j)(0-0)+hat(k)(32+32)`
`rArr L = 64 hat(k)` units.