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  • A cube of wood supporting a 200 g mass just floats in the water. When the mass is removed, the cube rises by 2 cm. What is the size (in cm) of the cube?Opti

A cube of wood supporting a 200 g mass just floats in the water. When the mass is removed, the cube rises by 2 cm. What is the size (in cm) of the cube?

Option: 1

5


Option: 2

15


Option: 3

10


Option: 4

20


Answers (1)

best_answer

 

 

 

 

The cube 'just floats' means that it is fully under water while floating.

 

 

   \begin{array}{l}{\text { Let } m \text { be the mass of the cube. Then }} \\ {\qquad(m+200) g=\ell^{3} \rho g . . . .(i)} \\ {\text { When the mass is removed, }} \\ {\qquad m g=(\ell-2) \ell^{2} \rho g . . . . (ii)} \\ {\text { Subtracting Eq. (ii) from Eq. (i), we have }} \\ {200=\rho\left[l^{3}-(l-2) l^2\right] \Rightarrow l=10 \mathrm{cm}(\text { using } \rho=1 \mathrm{g} / \mathrm{cc} \text { of water })}\end{array}

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Gunjita

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