Consider on elliptically shaped rail PQ in the vertical plane with OP = 3m and OQ = 4m. A block of mass 1kg is pulled along the rail from P to Q with a force of 18N, which is always parallel to line PQ as shown in figure. Assuming no frictional losses, then the kinetic energy of the block when it reaches ‘Q’ is $10 \times J$ . where $α =$ ............

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Detailed Solution

Work done by all forces = change in K.E

$ω_{F} + ω_{mg} = K_{F} - K_{i}$

$F_{s} - mgh = K_{F} (∵ K_{i} = 0)$

$18 (5) - 1 \times 10 \times 4 = K_{F}$

$K_{F} = 90 - 40 = 50$

In the question

$10 \propto = 50$

$\propto = 5$

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