A particle (m = 1 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 )) is : (Figure drawn is schematic and not to scale; take g = 10 ms-2)

Work Power and Energy PYQ — JEE Main 2020 · 7 Jan · Shift 1 · Q46 with Solution

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Correct answer: 10

Use conservation of mechanical energy on the frictionless track and during projectile motion

Since the track is frictionless and the particle moves freely under gravity afterward, total mechanical energy remains constant throughout the motion.

Initial state at point $A$

Mass: $m = 1\,\text{kg}$
Starts from rest, so initial kinetic energy: $K_A = 0$
Height of $A$ above reference level: $h_A = 2\,\text{m}$

So total energy at $A$ is only potential energy: $E = mgh_A = 1 \cdot 10 \cdot 2 = 20\,\text{J}$

State at highest point $P$

At the highest point of projectile motion, the height is given as: $h_P = 1\,\text{m}$

Potential energy at $P$ : $U_P = mgh_P = 1 \cdot 10 \cdot 1 = 10\,\text{J}$

Find kinetic energy at $P$

By conservation of mechanical energy: $K_P + U_P = E$ $K_P + 10 = 20$ $K_P = 10\,\text{J}$

Final answer

The kinetic energy of the particle at the highest point is: $\boxed{10}$

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