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A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2m). After reaching C, the particle continues to move freely in air as a projectile. When it reaches its highest point P (height 1m), the kinetic energy of the particle (in J) is: (Figure drawn is schematic and not to scale; take $$g = 10$$ ms$$^{-2}$$)
Correct Answer: 10
Total initial mechanical energy at point A: $$E_A = K_A + U_A = 0 + mgh_A$$
Total mechanical energy at the highest projectile point P: $$E_P = K_P + U_P = K_P + mgh_P$$
From conservation of mechanical energy ($$E_A = E_P$$): $$mgh_A = K_P + mgh_P \implies K_P = mg(h_A - h_P)$$
$$K_P = 1 \times 10 \times (2 - 1) = 10\text{ J}$$
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