A boy of mass 20 kg is standing on a 80 kg free to move long cart… | JEE Main 2013 (23 Apr, Shift 1)

Q9JEE Main 2013 · 23 APR · SHIFT 1Medium

Motion of Centre of Mass

A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart towards the wall, then the final distance of the boy from the wall will be

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Answer: (d)

No horizontal external force, so the CM stays fixed: $20\,x_b + 80\,x_c = 0$ (ground displacements).
The boy walks 10 m relative to the cart: $x_b - x_c = 10$ .
$x_c = -\frac{x_b}{4} \Rightarrow x_b + \frac{x_b}{4} = 10 \Rightarrow x_b = 8$ m towards the wall.
Final distance $= 25 - 8 = 17$ m, so the answer is (d).

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