Question

A vector of magnitude $10 \,N$ acting in $X Y$-plane has components $8\, N$ and $6\, N$ along positive $X$-axis and positive $Y$-axis, respectively. The coordinate system is rotated about $Z$-axis through angle $90^{\circ}$ in anti-clockwise direction. Find $x$-component and $y$-component in new coordinate system.

• A. $F_{x}=8\, N , F_{y}=6\, N$
• B. $F_{x}=6 \,N , F_{y}=8 \,N$
• C. $F_{x}=6\,N , F_{y}=-8 \,N$
• D. $F_{x}=8\, N , F_{y}=-6 \,N$

Answer 1

Answer: (C)

In new coordinate system,

$F \sin 37^{\circ}=6\, N$
$F \cos 37^{\circ}=8 \, N$
$x$-component $F_{x}=F \sin 37^{\circ}$
$=10 \times \frac{3}{5}=6 \, N$

$y$-component $F_{y}=-F \cos 37^{\circ}$
$=-10 \times \frac{4}{5}=-8\, N$