the resultant of two forces is ` 10 sqrt 13 N`, when one of the force is ` 10 sqrt 3 N` and angle between two forces is 1 30^@` then what is the value of second force ?

Options

A. ` 10 N`
B. ` 20 N`
C. ` 20 sqrt 23 N`
D. ` 10 sqrt 3 N`

Answer

B

Explanation

Here, ` R= 10 sqrt 13 N, A= 10 sqrt 3 N, theta = 30^@, B= ?`
` R^2 =B^2 + 2 = 2 zz 10 sqrt 3 xx B cos 30^@`
` (10 sqrt 13)^2 = ( 10 sqrt 3 )^2 + B^2 + 2 xx 10 sqrt 3 xx B cos 30^2`
` 1300 = + B^^@ = 30 B ` or B^2 + 30 B- 1000 =0`
` (B+ 50 ) (B- 20 ) = 0, B= 20 N ` or ` 50 N` ,