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A smooth track in the form of a quarter circle of radius \( 6 \mathrm{~m} \) lies in the vertical plane. A particle moves from \( P_{1} \) to \( P_{2} \) under the action of forces \( \vec{F}_{1}, \vec{F}_{2} \) and \( \vec{F}_{3} \). Force \( \vec{F}_{1} \) is always toward \( P_{2} \) and is always \( 20 \mathrm{~N} \) in magnitude. Force \( \vec{F}_{2} \) always acts horizontally and is always \( 30 \mathrm{~N} \) in magnitude. Force \( \vec{F}_{3} \) always acts tangentially to the track and is of magnitude \( 15 \mathrm{~N} \). Select the correct alternative(s)
(1) Work done by \( \vec{F}_{1} \) is \( 120 \mathrm{~J} \)
(2) Work done by \( \vec{F}_{2} \) is \( 180 \mathrm{~J} \)
(3) Work done by \( \vec{F}_{3} \) is \( 45 \pi \mathrm{J} \)
(4) \( \vec{F}_{1} \) is conservative in nature


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