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A particle (m = l kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in J) is : (Figure drawn is schematic and not to scale; take g = 10 ms^-2) $______$

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answer is 10.

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Detailed Solution

The energy throughout the entire travel will be conserved because the track AOC is frictionless and the gravitational force field is conservative.

Using the earth as the datum, where PE=0

${(PE + KE)}_{A} = {(PE + KE)}_{P} \Rightarrow {mgh}_{a} + 0 = {mgh}_{p} + {KE}_{p}$

${KE}_{p} = mg (h_{A} - h_{p}) = 1 \times 10 (2 - 1) = 10 J$

Hence the correct answer is 10J.

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