A point like object of mass \( \mathrm{m} \) starts from point \( \...

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A point like object of mass \( \mathrm{m} \) starts from point \( \mathrm{K} \) as shown in the figure. It slides inside along the full length of the smooth track of radius \( \mathrm{R} \), and then moves freely and travels to point \( \mathrm{C} \). [The track is kept in vertical plane]
Find the normal force exerted by the track at point A.
(A) \( \mathrm{F}_{\mathrm{A}}=m g\left(\frac{\mathrm{d}^{2}}{2 \mathrm{R}^{2}}-2\right) \)
(B) \( \mathrm{F}_{\mathrm{A}}=m g\left(\frac{\mathrm{d}^{2}}{2 \mathrm{R}^{2}}+2\right) \)
(C) \( \mathrm{F}_{\mathrm{A}}=m g\left(\frac{3 \mathrm{~d}^{2}}{\mathrm{R}^{2}}+2\right) \)
(D) \( \mathrm{F}_{\mathrm{A}}=m g\left(\frac{\mathrm{d}}{3 \mathrm{R}^{2}}+2\right) \)
\( \mathrm{P} \)
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