KCET · Physics · Mathematics in Physics
The \(X\) and \(Y\) components of a force \(F\) acting at \(30^{\circ}\) to \(x\)-axis are respectively
- A \(\mathrm{F}, \frac{\mathrm{F}}{\sqrt{2}}\)
- B \(\frac{F}{\sqrt{2}}, \mathrm{~F}\)
- C \(\frac{\mathrm{F}}{2}, \frac{\sqrt{3}}{2} \mathrm{~F}\)
- D \(\frac{\sqrt{3}}{2} \mathrm{~F}, \frac{1}{2} \mathrm{~F}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{3}}{2} \mathrm{~F}, \frac{1}{2} \mathrm{~F}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{F}_{\mathrm{x}}=\mathrm{F} \cos 30^{\circ}=\frac{\sqrt{3}}{2} \mathrm{~F} \)
\(\mathrm{F}_{\mathrm{y}}=\mathrm{F} \sin 30^{\circ}=\frac{1}{2} \mathrm{~F}\)
\(\mathrm{F}_{\mathrm{y}}=\mathrm{F} \sin 30^{\circ}=\frac{1}{2} \mathrm{~F}\)
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