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Q. No.

A wooden block is initially floating in a bucket of water with \(\frac{4}{5}\)​ of its volume submerged. When a certain amount of oil is poured into the bucket, the block is found to be just under the oil surface with half of its volume submerged in water and half in oil. What is the density of the oil relative to that of water?
1. \(0.7\)
2. \(0.5\)
3. \(0.8\)
4. \(0.6\)

Subtopic:  Archimedes' Principle |
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A cubical block of side \(0.5\) m floats on water with \(30\)% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it underwater?
(take, density of water \(=10^3\) kg/m3)
1. \(30.1\) kg
2. \(87.5\) kg
3. \(65.4\) kg
4. \(46.3\) kg

Subtopic:  Archimedes' Principle |
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A air bubble of radius \(1\) cm in water has an upward acceleration \(9.8~\text{cm} \text{s}^{-2}\). The density of water is \(1~\text{gm} \text{cm}^{-3}\) and water offers negligible drag force on the bubble. The mass of the bubble is: (\(g = 980\) cm/s2 )
1. \(3.15 ~\text{gm}\)
2. \(1.52 ~\text{gm}\)
3. \(4.51 ~\text{gm}\)
4. \(4.15~\text{gm}\)

Subtopic:  Archimedes' Principle |
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A hollow spherical shell of outer radius \(R\) floats just submerged beneath the surface of water. The inner radius of the shell is \(r.\) If the specific gravity of the shell material with respect to water is \(\dfrac{27}{8},\) what is the value of \(r\text{?}\)
\( \left (\text{use:}~19^{1/3}= \dfrac{8}{3}\right )\)

1. \(\dfrac{4}{9}R\) 2. \(\dfrac{8}{9}R\)
3. \(\dfrac{1}{3}R\) 4. \(\dfrac{2}{3}R\)
Subtopic:  Archimedes' Principle |
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A drop of liquid of density \(\rho\) is floating half immersed in a liquid \(\sigma \) and surface tension \(7.5 \times 10^{-4} \mathrm{Ncm}^{-1}\). The radius of drop in cm will be : ( Take g = 10 m/s2)
1. \({15 \over \sqrt {2 \rho - \sigma}}\)
2. \({15 \over \sqrt {\rho - \sigma}}\)
3. \({3 \over2 \sqrt { \rho - \sigma}}\)
4. \({3 \over20 \sqrt {2 \rho - \sigma}}\)
Subtopic:  Archimedes' Principle |
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A sphere of relative density \(\sigma\) and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank is :
1. \(\left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}\)
2. \(\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}\)
3. \(\left(\frac{\sigma-2}{\sigma+2}\right)^{1 / 3}\)
4. \(\left(\frac{\sigma+1}{\sigma-1}\right)^{1 / 3}\)
Subtopic:  Archimedes' Principle |
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A load of mass \(M~\text{kg}\) is suspended from a steel wire of length \(2~\text{m}\) and radius \(1.0~\text{mm}\) in Searle’s apparatus experiment. The increase in length produced in the wire is \(4.0~ \text{mm.}\) Now the load is fully immersed in a liquid of relative density \(\mathrm{2. }\)The relative density of the material of the load is \(\mathrm{8.}\) The new value of the increase in length of the steel wire is:
1. \(3.0~\text{mm}\)
2. \(4.0~\text{mm}\)
3. \(5.0~\text{mm}\)
4. zero
Subtopic:  Archimedes' Principle |
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Consider a solid sphere of radius \(R\) and mass density \(p(r)=p_0\left(1-\frac{r^2}{R^2}\right), 0<r \leq R.\) The minimum density of a liquid in which it will float is:
1. \(\dfrac{{p}_0}{5}\)

2. \(\dfrac{2 p_0}{5}\)

3. \(\dfrac{2 p_0}{3}\)

4. \(\dfrac{{p}_0}{3}\)
Subtopic:  Archimedes' Principle |
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A leakproof cylinder of length \(1 ~\text m ,\) made of a metal which has a very low coefficient of expansion is floating vertically in water at \(0^\circ\text {C}\) such that its height above the water surface is \(20 ~\text{cm}.\) When the temperature of the water is increased to \(4^\circ\text{C}\) the height of the cylinder above the water surface becomes \(21 ~\text{cm} .\) The density of water at \({T}=4^\circ \text C,\) relative to the density at \(T=0^\circ \text C\) is close to:
1. \(1.01\)
2. \(1.26\)
3. \(1.04\)
4. \(1.03\)
Subtopic:  Archimedes' Principle |
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An ice block of density \(\text{0.9 g/cc}\) is sub-merged as shown in the figure. The density of oil is \(\text{0.8 g/cc},\) the density of water is \(\text{1 g/cc}\) and the volume inside the water and oil is \(V_2\) and \(V_1\) respectively the ratio of volumes \(\frac{V_1}{V_2}\) is:
 
1. \(5\)
2. \(3\)
3. \(1\)
4. \(6\)
 
Subtopic:  Archimedes' Principle |
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