A boy of mass 20, kg is standing on an 80, kg | vedclass

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(D) Since there is no external horizontal force acting on the system,the center of mass of the boy-cart system remains stationary relative to the grou

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$17$

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(D) Since there is no external horizontal force acting on the system,the center of mass of the boy-cart system remains stationary relative to the ground.Let $m_1 = 20\, kg$ be the mass of the boy and $m_2 = 80\, kg$ be the mass of the cart.Let the boy move $10\, m$ towards the wall relative to the cart. Let the cart move a distance $x$ away from the wall relative to the ground.The displacement of the boy relative to the ground towards the wall is $\Delta x_1 = 10 - x$.The displacement of the cart relative to the ground away from the wall is $\Delta x_2 = -x$.Using the center of mass displacement formula: $m_1 \Delta x_1 + m_2 \Delta x_2 = 0$.$20(10 - x) + 80(-x) = 0$.$200 - 20x - 80x = 0$.$100x = 200 \implies x = 2\, m$.The net displacement of the boy towards the wall relative to the ground is $\Delta x_1 = 10 - 2 = 8\, m$.The final distance of the boy from the wall is $25 - 8 = 17\, m$.

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