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  4. 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 J) is: (Figure drawn is schematic and not to scale; take g = 10 ms-2) .

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Q. 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 J) is : (Figure drawn is schematic and not to scale; take $g = 10\, ms^{-2}$) __________ .Physics Question Image

JEE MainJEE Main 2020Work, Energy and Power

Solution:

As the track $AOC$ is frictionless and the force field is gravitational is conservative so the energy along the whole motion will be conserved.
Taking ground as datum where $P E =0$
$( PE + KE )_{ A }=( PE + KE )_{ p }$
$\Rightarrow mgh _{ a }+0= mgh _{ p }+ KE _{ p }\left(\operatorname{as} v = o\right.$ at $\left.A \operatorname{so} KE _{ A }\right)$
$\Rightarrow KE _{ P }= mg \left( h _{ A }- h _{ p }\right)$

$KE _{ p }=10 J $