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Q. No.An ice berg of density 900 Kg/ is floating in water of density 1000 Kg/. The percentage of volume of ice-cube outside the water is
1. 20%
2. 35%
3. 10%
4. 25%
(density of water \(=10^{3}~\text{kg/m}^3\))
1. \(750\)
2. \(1000\)
3. \(1250\)
4. \(1500\)
In the making of an alloy, a metal of density \(n_1\) and another metal of density \(n_2\) are used. If the masses of the two metals used are \(m_1\) and \(m_2\) respectively, then the density of the alloy is:
1. \( \left(\frac{\mathrm{m}_1+\mathrm{m}_2}{\mathrm{n}_1+\mathrm{n}_2}\right) \)
2. \( \frac{\mathrm{m}_1+\mathrm{m}_2}{\left(\frac{\mathrm{m}_1}{\mathrm{n}_1}+\frac{\mathrm{m}_2}{\mathrm{n}_2}\right)}\)
3. \( \frac{\mathrm{m}_1+\mathrm{m}_2}{\left(\frac{\mathrm{m}_1+\mathrm{m}_2}{\mathrm{n}_2+\mathrm{n}_1}\right)} \)
4. \( \left(\frac{\mathrm{n}_1+\mathrm{n}_2}{2}\right) \)
A metal block floats at the interface of two liquids with \(\frac13\) of its volume in the upper liquid \((A)\) and \(\frac23\) in the lower liquid \((B).\) The densities of the metal, liquid \(A,\) and liquid \(B\) are \(\rho,~ \rho_{\Large_A}~, \rho_{\Large_B}\) respectively. Then:
| 1. | \(\rho_{\Large_B}=2\rho_{\Large_A}\) | 2. | \(\rho=\frac13\rho_{\Large_A}+\frac23\rho_{\Large_B}\) |
| 3. | \(\rho=\frac23\rho_{\Large_A}+\frac13\rho_{\Large_B}\) | 4. | \(\rho=\frac13\sqrt{\rho_{\Large_A}\rho_{\Large_B}}\) |
The density of the material of the cylinder is:
1. \(1.5\rho\)
2. \(1.25\rho\)
3. \(1.8\rho\)
4. \(1.75\rho\)
\(15\%\) volume of a cubical block is outside water. The relative density of the block is:
1. \(0.15\)
2. \(0.30\)
3. \(0.60\)
4. \(0.85\)
The net force of buoyancy on the cylinder due to the two liquids equals:
| 1. | \(mg\) | 2. | \(\dfrac{mg}{2}\) |
| 3. | \(\dfrac{3mg}{2}\) | 4. | \(\dfrac{4mg}{3}\) |
| 1. | \(\dfrac{x}{y}\) | 2. | \(\dfrac{y}{x}\) |
| 3. | \(\dfrac{x}{{x}{-}\left({{z}{-}{y}}\right)}\) | 4. | \(\dfrac{x}{{x}{-}{z}}\) |
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Q. No.
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