Question

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

• A. $F_x=8N,F_y=8N$
• B. $F_x=6N,F_y=-8N$
• C. $F_x=0N,F_y=10N$
• D. $F_x=6N,F_y=8N$

Answer 1

The correct option is B $F_x=6N,F_y=-8N$

Draw a rough sketch of the component of $10N$ force.

Find $x$ and $y-$components of the force.
It is clear from the diagram
$F\sin {37}^{\circ }=6N$
$\&F\cos {37}^{\circ }=8N$

Find $x$ and $y-$components of the force when coordinate system is rotated about $z-$axis through angle ${90}^{\circ }$.
This situation can be drawn as
Now $x$ and $y-$components of the force
$F_x=F\sin {37}^{\circ }=10\times \frac{3}{5}=6N$ and $F_y=F\cos {37}^{\circ }=10\times \frac{4}{5}=-8N$
Final Answer: (c)