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A particle of mass \( m \) is projected with speed \( \mathrm{v}_{0}=\sqrt{\frac{R \mathrm{~g}}{4}} \) from top of a smooth hemisphere as shown in figure, then
(1) particle will leave contact with hemisphere at
\[
\theta=\cos ^{-1}\left(\frac{2}{3}\right)
\]
(2) particle will leave contact with hemisphere at
\[
\theta=\cos ^{-1}\left(\frac{3}{4}\right)
\]
(3) particle will leave contact with hemisphere at
\[
\theta=\sin ^{-1}\left(\frac{2}{3}\right)
\]
(4) particle will leave contact with hemisphere at
\[
\theta=\sin ^{-1}\left(\frac{3}{4}\right)
\]
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