The resultant of two forces is 20 N when one of force is 20`sqrt(3)` N and angle between two forces is 30° then what is value of second force ?

Options

A. 10N
B. 20N
C. `20sqrt(3)N`
D. `10sqrt(3)N`

Answer

B

Explanation

`R^(2)=A^(2)+B^(2)+2ABostheta`
`(20)^(2)=(20sqrt(3))^(2) +B^(2)+2xx20sqrt(3)Bxxsqrt(3)/2`
`(20)^(2)=1200+B^(2)+20sqrt(9)B`
`-800=B^(2)+60B` or `B^(2)+60B+800=0`
Solving the quadratic equation B = 20 N