Q. No.A tub is filled with water and a wooden cube \(10\) cm \(\times10\) cm \(\times 10\) cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \(3.87\) cm. The mass of the metal coin is: (in gram)
(Take water density as \(1~\text{g/cm}^3\) and density of wood as \(0.4~\text{g/cm}^3\))
1. \(387\)
2. \(400\)
3. \(240\)
4. \(300\)
(Take water density as \(1~\text{g/cm}^3\) and density of wood as \(0.4~\text{g/cm}^3\))
1. \(387\)
2. \(400\)
3. \(240\)
4. \(300\)
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A cubical block of density \(\rho_{b}= 600~\text{kg/m}^3\) floats in a liquid of density \(\rho_{e} = 900~\text{kg/m}^3\). If the height of block is \(H=8.0~\text{cm} \) then height of the submerged part is: (in cm)
1. \(7.3 \)
2. \(4.3\)
3. \(6.3\)
4. \(5.3\)
1. \(7.3 \)
2. \(4.3\)
3. \(6.3\)
4. \(5.3\)
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A cube having a side of \(10~\text{cm}\) with unknown mass and \(200~\text{gm}\) mass were hung at two ends of an uniform rigid rod of \(27~\text{cm}\) long. The rod along with masses was placed on a wedge keeping the distance between wedge point and \(200~\text{gm}\) weight as \(25~\text{cm}.\) Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1~\text{gm/cm}^3 .\))
The unknown mass is: (in kg)
1. \(3\)
2. \(7\)
3. \(9\)
4. \(10\)
The unknown mass is: (in kg)
1. \(3\)
2. \(7\)
3. \(9\)
4. \(10\)
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A \(400~\text g\) solid cube having an edge of length \(10~ \text{cm}\) floats in water. How much volume of the cube is outside the water?(Given: density of water \(=1000~\text{kg}~\text m^{-3} )\)
1. \(4000~\text{cm}^3\)
2. \(1400~\text{cm}^3\)
3. \(600~\text{cm}^3\)
4. \(400~\text{cm}^3\)
1. \(4000~\text{cm}^3\)
2. \(1400~\text{cm}^3\)
3. \(600~\text{cm}^3\)
4. \(400~\text{cm}^3\)
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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. \(\left(\frac{\sigma+1}{\sigma-1}\right)^{1 / 3}\)
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. \(\left(\frac{\sigma+1}{\sigma-1}\right)^{1 / 3}\)
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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. \(6\)
1. \(5\)
2. \(3\)
3. \(1\)
4. \(6\)
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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. \({3 \over20 \sqrt {2 \rho - \sigma}}\)
1. \({15 \over \sqrt {2 \rho - \sigma}}\)
2. \({15 \over \sqrt {\rho - \sigma}}\)
3. \({3 \over2 \sqrt { \rho - \sigma}}\)
4. \({3 \over20 \sqrt {2 \rho - \sigma}}\)
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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. \(1.03\)
1. \(1.01\)
2. \(1.26\)
3. \(1.04\)
4. \(1.03\)
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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. \(\dfrac{{p}_0}{3}\)
1. \(\dfrac{{p}_0}{5}\)
2. \(\dfrac{2 p_0}{5}\)
3. \(\dfrac{2 p_0}{3}\)
4. \(\dfrac{{p}_0}{3}\)
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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. \(4.15~\text{gm}\)
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