Question

Two forces of magnitude 15F and 30F are acting on a body in the same direction. Their resultant force is 150N.find the value of F​

Answer 1

Given,

Two forces of magnitude 15F and 30F

and both were acting in same direction.

As per the question,

Sum of forces = resultant Force  

15F + 30F = 150

15(  F + 2F) = 150

15 ( 3F) = 150

3F = $\frac{150}{15}$

F = $\frac{10}{3}$

∴ The value of F is  10/3.

Answer 2

Two forces of magnitude 15F and 30F are acting on a body in the same direction.

i.e., Angle between them ,A = 0°

Resultant force = 150 N

$\sqrt{ {15F}^{2} + {30 F}^{2} + 2 \times 15 F \times 30 F \cos(A) }$ = 150 N

$\sqrt{ {15F}^{2} + {30 F}^{2} + 2 \times 15 F \times 30 F \cos(0) }$ = 150 N

$\sqrt{ {15F}^{2} + {30 F}^{2} + 2 \times 15 F \times 30 F }$ = 150 N

$\sqrt{ {(15F + 30F)}^{2} }$ = 150 N

15F + 30F = 150N

45F = 150N

F = 150N / 45

F = 10N/3

So , the value of F is 10N/ 3.