Question

04) A force of 40N has one of the rectangular
component as 20./3 N. The another
rectangular component will be__
A) 25 N
B) 10 N
C) 20 N
D) 30 N​

Answer 1

Let our force be,

$\longrightarrow\vec F=F_x\,\hat i+F_y\,\^j$

where $F=40\ N$ and $F_x=20\sqrt3\ N.$ We have to find $F_y.$

Then,

$\longrightarrow |\vec F|=40$

$\longrightarrow \sqrt{(F_x)^2+(F_y)^2}=40$

$\longrightarrow \sqrt{(20\sqrt3)^2+(F_y)^2}=40$

$\longrightarrow \sqrt{1200+(F_y)^2}=40$

$\longrightarrow 1200+(F_y)^2=1600$

$\longrightarrow (F_y)^2=400$

$\longrightarrow\underline{\underline{F_y=20\ N}}$

Thus (C) 20 N is the answer.