Question

Two like parallel forces are acting at a distance of 24 mm apart and their resultant is 20 N. It the line of action of the resultant is 6 mm from any given force, the two forces are
A.15 N and 5 N
B.20 N and 5 N
C. 15 N and 15 N
D.none of these

Answer 1

F1+F2=20--------(1)

F1(24-6)-F2(6)=0--(2)

18F1-6F2=0

18F1=6F2

F1/F2=6/18

F1/F2=1/3

Now 1:3 ratio

F1=5,F2=15

Answer 2

answer : option (A) 15N and 5N

explanation : Let F1 and F2 are two parallel force acting at a distance of 24mm apart and their resultant is 20N.

so, √{F1² + F2² +2F1.F2cos0°} = 20N [ as forces are parallel so, angle between them is 0°

or, √(F1 + F2)² = 20N

or, F1 + F2 = 20N......(1)

now, the line of action of the resultant is 6mm from the given force.

if we assume F1 > F2 , then line of action will be near of F1 . Let R is the point where line of action is appear.

i.e., F1.....(6mm)....R......(18mm).....F2

net torque at R should be zero.

so, 0 = F1 × 6mm(→) + F2 × 18mm(←)

or, 6F1 - 18F2 = 0....(2)

from equations (1) and (2),

F1 = 15N and F2 = 5N.