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A smooth track in form of a quarter circle of radius 6 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 towards $P_{2}$ and is always 20 N in magnitude. Force ${\vec{F}}_{2}$ is always act horizontally and is always 30 N in magnitude. Force ${\vec{F}}_{3}$ always acts tangentially to the track and is of magnitude 15 N. select the correct magnitude.

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Work done by ${\vec{F}}_{1}$ is $120 \sqrt{2} J$

Work done by ${\vec{F}}_{2}$ is 180J

Work done by ${\vec{F}}_{3}$ is $45 π J$

${\vec{F}}_{3}$ is conservative in nature.

answer is A, B, C.

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Detailed Solution

$ω_{F_{2}} = F_{2} (S) = 180 J ω_{F_{2}} = 15 \frac{π R}{2} = 45 J ω_{F_{1}} = 120 \sqrt{2} J$

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