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A particle moving in a circle of radius \( \mathrm{R} \) with a uniform speed takes a time \( \mathrm{T} \) to complete …

Q1

A particle moving in a circle of radius \( \mathrm{R} \) with a uniform speed takes a time \( \mathrm{T} \) to complete one revolution. If this particle were projected with the same speed at an angle \( \theta \) to the horizontal, the maximum height attained by it equals \( 4 \mathrm{R} \). The angle of projection, \( \theta \), is then given by:

[NEET 2021]

a

\( \theta=\cos ^{-1}\left(\frac{\pi^{2} \mathrm{R}}{\mathrm{gT}^{2}}\right)^{1 / 2} \)

b

\(\theta ={\sin }^{-1}{\left(\frac{{\pi }^{2}\mathrm{R}}{{\mathrm{gT}}^{2}}\right)}^{1/2}\)

c

\( \theta=\sin ^{-1}\left(\frac{2 g \mathrm{~T}^{2}}{\pi^{2} \mathrm{R}}\right)^{1 / 2} \)

d

\( \theta=\cos ^{-1}\left(\frac{\mathrm{gT}^{2}}{\pi^{2} \mathrm{R}}\right)^{1 / 2} \)

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