Two solid spheres A and B of equal volumes bu | vedclass

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(A) Let $V$ be the volume of each sphere.For the equilibrium of sphere $A$:The forces acting on $A$ are the buoyant force $V d_F g$ upwards,the weight

Vedclass · Accepted Answer

$(A, B, C)$

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(A) Let $V$ be the volume of each sphere.For the equilibrium of sphere $A$:The forces acting on $A$ are the buoyant force $V d_F g$ upwards,the weight $V d_A g$ downwards,and the tension $T$ in the string downwards.$V d_F g = V d_A g + T$$T = V g (d_F - d_A)$Since the string must have tension $T > 0$,we must have $d_F > d_A$,or $d_A For the equilibrium of sphere $B$:The forces acting on $B$ are the buoyant force $V d_F g$ upwards,the weight $V d_B g$ downwards,and the tension $T$ in the string upwards.$T + V d_F g = V d_B g$$T = V g (d_B - d_F)$Since the string must have tension $T > 0$,we must have $d_B > d_F$.Equating the two expressions for tension $T$:$V g (d_F - d_A) = V g (d_B - d_F)$$d_F - d_A = d_B - d_F$$d_A + d_B = 2 d_F$Thus,the conditions $(A)$,$(B)$,and $(C)$ must all be satisfied for this equilibrium to exist.

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