A smooth track in the form of a quarter circle of radius 6m lies in the vertical plane. A particle moves from P1 to P2 under the action of forces F→1, F→2 and F→3. Force F1 is always toward P2 and is always 20 N in magnitude. Force F→2 always acts horizontally and is always 30 N in magnitude. Force F→3 always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)

Work done by F→1 is W1=∫P1P2 F1cos⁡θdsWhere, ds=(6)d(−2θ)=−12dθ and F1=20N⇒W1=−240∫π/40 cos⁡θdθ⇒W1=240sin⁡π4=1202JF→1 is conservative because it is always directed towards a fixed point P2. Therefore, W1 can be directly calculated asW1=F1P1P2=(20)(62)=1202JSimilarly, W2=F2OP2=(30)(6)=180 Jand W3=∫06(π/2) F3ds=∫03π 15ds W3=15s03π=45π J

A smooth track in the form of a quarter circle of radius 6m lies in the vertical plane. A particle moves from P1 to P2 under the action of forces F→1, F→2 and F→3. Force F1 is always toward P2 and is always 20 N in magnitude. Force F→2 always acts horizontally and is always 30 N in magnitude. Force F→3 always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)

Work done by F→1 is W1=∫P1P2 F1cos⁡θdsWhere, ds=(6)d(−2θ)=−12dθ and F1=20N⇒W1=−240∫π/40 cos⁡θdθ⇒W1=240sin⁡π4=1202JF→1 is conservative because it is always directed towards a fixed point P2. Therefore, W1 can be directly calculated asW1=F1P1P2=(20)(62)=1202JSimilarly, W2=F2OP2=(30)(6)=180 Jand W3=∫06(π/2) F3ds=∫03π 15ds W3=15s03π=45π J