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 center of the submerged portion is above the center of mass of the object). The value of N is closest to

Question

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 center of the submerged portion is above the center of mass of the object). The value of N is closest to, 6, 10, 16, 24

MARKS App · Accepted Answer

Let mass of each coin be m . ∴ Location of center of mass after N coins are kept on lid from bottom of container is 40 m × 0 + Nm × 9 40 + N m = 9 N 40 + N cm Also height of submerged portion after keeping N coins on lid will be, 3 40 + N 40 cm ∴ Equilibrium will just be stable if 3 40 40 + N 2 = 9 N 40 + N ⇒ 3 N 2 - 480 N + 4800 = 0 ⇒ N = 10 . 72

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