KVPY 2020-21 SA Exam Previous Papers

Question : 69 of 80

Marks: +1, -0

A wide bottom cylindrical massless plastic container of height 9 cm has 40 identical coins inside it and is floating on water with 3 cm inside the water. If we start putting more of such coins on its lid, it is observed that after N coins are put, its equilibrium changes from stable to unstable. Equilibrium in floating is stable if the geometric centre of the submerged portion is above the centre of the mass of the object). The value of N is closed to

Validate

Solution:

For unstable equilibrium
C.O.M of system ≥ geometric centre of submerged part

{9 N}/{N+40} \≥{y}/{2}

(N+40) m g=y \×A \ρg

Initial condition

40 {mg}=3 \×{A} \ρ{g}

(N+40) {mg}={y \×40 {mg}}/{3}

y={3(N+40)}/{40}

{9 N}/{N+40}={3(N+40)}/{80}

240 N=(N+40)^{2}

240 N=N^{2}+80 N+1600

N^{2}-160 N+1600=0

On solving

N \≈10.7,149.28

Final answer is 10.

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