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A iron ball is suspended by a thread of negligible mass from a partially floating upright cylinder. The cylinder has a face area of $12 \ \ \mathrm{cm}^2$, height of $6.0 \ \ \mathrm{cm}$ and density $0.25 \ \ \mathrm{g/cm}^3$. If the top of cylinder is $1.0 \ \ \mathrm{cm}$ above water, find the radii of the iron ball ?

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From FBDs I get,

$$T + f_b = mg \tag{1}$$ $$F_b = Mg + T \tag{2}$$ From $(1)\ and \ (2)$, $$F_b - Mg + f_b = mg$$ $$ \rho_w V_{c,s}g - \rho_c V_{c}g + \rho_w V_{b}g = \rho_b V_{b}g$$ $$ \rho_w V_{c,s} - \rho_c V_{c} + \rho_w V_{b} = \color{red}{\rho_b} V_{b}$$

Before I go ahead, I don't know how can get the value of $\rho_b$, which is not given.Without the value of $\rho_b$ I can't solve the equation.

The given answer is $1.1 \ \ \mathrm{cm}$ and with that I try to find the density of ball, which comes out to $8.533 \ \ \mathrm{g/cm}^3$. The density of iron is $8 \ \ \mathrm{g/cm}^3$.

I feel that the question is incomplete and density of the ball should have been given.

I need a second opinion.

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  • $\begingroup$ Often in a Physics problem, if the material is stated you can use that material's physical characteristics in the problem, such as its density. You are correct that the density is needed to solve the problem. $\endgroup$ – Paul Jan 16 '17 at 13:52
  • $\begingroup$ Yes. I think so. $\endgroup$ – Paul Jan 16 '17 at 13:55
  • $\begingroup$ Of course this problem can't be solve w/o the density of the ball. $\endgroup$ – Gert Jan 16 '17 at 14:08
  • $\begingroup$ @Gert Maybe obvious to you but not for me. $\endgroup$ – A---B Jan 16 '17 at 16:00
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Often in a Physics problem, if the material name is stated you can use that material's physical characteristics in the problem, such as its density. You are correct that the density is needed to solve the problem. Note that you used the density of water without it being expressly given. You have the right approach, and given the density of iron you can solve it with your equations.

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  • $\begingroup$ Note that "iron" describes a range of materials with quite a variation in density. A "reasonable" assumption of density should result in an acceptable answer. $\endgroup$ – Floris Jan 16 '17 at 15:35

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