Question

Two forces of magnitude 20N and 50N act simultaneously on a body. Which one of the following forces can not be a resultant of the two forces? A.: ; 20 N B.( ) 30 N C.C_i 40 N D.,_,; 70 N

Answer 1

Two forces of magnitude 20N and 50N act simultaneously on a body.

To check : which one of the forces cannot be a resultant of the two forces ?

A. 20N B. 30N C. 40N D. 70N

solution : we know, resultant of two forces A and B is given by,

R = √{A² + B² + 2ABcosθ}, where θ is the angle between A and B.

we also know, -1 ≤ cosθ ≤ 1

so, when cosθ = -1, minimum value of R = |A - B|

when cosθ = 1 , maximum value of R = |A + B|

i.e., |A - B| ≤ R ≤ |A - B| ,

applying this concept here.

A = 20 N, B = 50N

then, |20 - 50| ≤ R ≤ |20 + 50|

⇒30 ≤ R ≤ 70

here it is clear that resultant of 20N and 50N can't be less than 30N and greater than 70N.

so, option (A) is correct choice.