Question

Which of the following pairs of forces cannot be added to give a resultant force of $4N$?

• A. $2N$ and $8N$
• B. $2N$ and $2N$
• C. $2N$ and $6N$
• D. $2N$ and $4N$

Answer 1

The correct option is A $2N$ and $8N$

Resultant force,

$F=\sqrt{F_1^2+F_2^2+2F_1{F}_{2}cos\theta }$. . . . . . . . .(1)

Lets consider the option A,

$F_1=2N$

$F_2=8N$

For maximum resultant force, $cos\theta =1$

From equation (1),

$F_{max}=\sqrt{F_1^2+F_2^2+2F_1{F}_2}=\sqrt{(F_1+F_2{)}^2}$

$F_{max}=F_1+F_2$

$F_{max}=8+2=10N$

For minimum resultant force, $cos\theta =-1$

$F_{min}=\sqrt{F_1^2+F_2^2-2F1F_2}=\sqrt{(F_1-F_2{)}^2}$

$F_{min}=\sqrt{(2-8{)}^2}=6N$

So, the $4N$ does not lie within this range. Thus it is not possible to have it as resultant force.

The correct option is A.