Question

Two balls are rolling on a flat smooth table. One ball has velocity components `sqrt(3) hat(j)` and `hat(i)` while the other has components `2 hat(i)` and `2 hat(j)`. If both start moving simultaneously from the same point, the angle between their paths is-
A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer 1

Correct Answer - A
Velocity of one ball `vec(v)_(1)=hat(i)+sqrt(3)hat(j)`
Velocity od second ball `vec(v)_(2)=2hat(i)+2hat(j)`
Angle between their path:
`cos theta=(vec(v)_(1).vec(v)_(2))/(v_(1)v_(2))=(2+2sqrt(3))/((2)(2sqrt(2)))=(1+sqrt(3))/(2sqrt(2))rArr theta=15^(@)`