Density

Q. Mass is non-uniformly distributed on the circumference of a ring of radius $\alpha$ and center at origin. let $b$ the disatnce of center of mass of the ring from origin

1. $b<\alpha$
2. $0\le b\le \alpha$
3. $b>\alpha$
4. $b=\alpha$

Q. A body weighs $50\text{g}$ in air and $40\text{g}$ when completely immersed in water. How much it will weigh when immersed completely in a liquid of relative density $1.5$?

1. $30\text{g}$
2. $35\text{g}$
3. $45\text{g}$
4. $25\text{g}$

Q. Density of a mixture is $\rho$, when fluids of densities ${\rho }_1\text{and}{\rho }_2$ are mixed in the same proportion. Then:

1. $\rho =\frac{{\rho }_1+{\rho }_2}{2}$
2. $\rho =\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$
3. $\rho =\frac{{\rho }_1^2}{{\rho }_2}$
4. $\rho =\frac{{\rho }_2^2}{{\rho }_1}$

Q. Three liquids of densities $d,2d$ and $3d$ are mixed in equal proportions of weights. What is the relative density of the mixture, if $d$ is the density of water?

1. $\frac{11}{7}$
2. $\frac{18}{11}$
3. $\frac{13}{9}$
4. $\frac{23}{18}$

Q. The centre of mass of a solid hemisphere of radius $8\text{cm}$ is $x\text{cm}$ from the centre of the flat surface. Then value of $x$ is ______.

Q. The density of alcohol is $780{\text{kg/m}}^3$. Its relative density is

1. $7.8{\text{g/cm}}^3$
2. $7.8$
3. $7.8{\text{kg/m}}^3$
4. $0.78$

Q. The density of a solid metal sphere is determined by measuring its mass and its diameter, the maximum error in the density of the sphere is $\left(\frac{x}{100}\right)$%. If the relative errors in measuring the mass and the diameter are $6.0\text{\%}$ and $1.5\text{\%}$ respectively, the value of $x$ is

Q. Two substances of relative densities ${\rho }_1$ and ${\rho }_2$ are mixed in equal volumes and the relative density of the mixture is $4$. When they are mixed in equal masses, the relative density of the mixture is $3$. The values of ${\rho }_1$ and ${\rho }_2$ are

1. ${\rho }_1=6$ and ${\rho }_2=2$
2. ${\rho }_1=3$ and ${\rho }_2=5$
3. ${\rho }_1=12$ and ${\rho }_2=4$
4. None of these

Q. 1 kilogram of cotton and 1 kilogram of iron are weighed in a vacuum then which one of them will be more.

Q. A uniform solid hemisphere of radius R is immersed into a liquid of density \(\rho\) as shown. The base of the hemisphere is at distance R from the surface of the liquid. Ignore atmospheric pressure. The force by the liquid on the curved surface of the hemisphere is

Q.

Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass M of ice melts

1. 

2. 

3. 

4. 

Q. A bat used in sports of cricket is cut at the location of its centre of mass shown in the figure. Then

1. the masses of both the pieces will be same
2. mass of part II would be larger
3. mass of part I would be thrice the mass of part II
4. mass of part I would be larger

Q. A piece of solid weighs $120\text{g}$ in air and $80\text{g}$ when completely immersed in water. The relative density of solid is

1. $\frac{3}{2}$
2. $\frac{4}{3}$
3. $3$
4. $2$

Q.

Suppose the tube in the previous problem is kept vertical with A upward but the other conditions remain the same. The separation between the cross sections at A and B is $\frac{15}{16}$ cm. Repeat parts (a), (b) and (c) of the previous problem. Take g = 10 m$s^{-2}$.

Q. A simple pendulum of mass ${}^{\prime }{m}^{\prime }$, length ${}^{\prime }{l}^{\prime }$ and charge ${}^{\prime }+q^{\prime }$ suspended in the electric field produced by two conducting parallel plates as shown in the figure. The value of deflection of pendulum in equilibrium position will be
$(C_1$ and $C_2$ are the capacitance of capacitors formed by parallel plates, without medium in between and with medium in between, respectively.$)$

1. ${\tan }^{-1}[\frac{q}{mg}\times \frac{C_1(V_2-V_1)}{(C_1+C_2)(d-t)}]$
2. ${\tan }^{-1}[\frac{q}{mg}\times \frac{C_2(V_2-V_1)}{(C_1+C_2)(d-t)}]$
3. ${\tan }^{-1}[\frac{q}{mg}\times \frac{C_2(V_1+V_2)}{(C_1+C_2)(d-t)}]$
4. ${\tan }^{-1}[\frac{q}{mg}\times \frac{C_1(V_1+V_2)}{(C_1+C_2)(d-t)}]$

Q. Two liquids $A$ and $B$ are at ${30}^{\circ }C$ and ${20}^{\circ }C$, respectively. When they are mixed in equal masses, the temperature of the mixture is found to be ${26}^{\circ }C$. The ratio of their specific heat is

1. $2:3$
2. $4:3$
3. $3:4$
4. $3:2$

Q. Three liquids of densities $d,2d$ and $3d$ are mixed in equal volumes. Then the density of the mixture is

1. $d$
2. $3d$
3. $5d$
4. $2d$

Q. $5g$ of steam at ${100}^{\circ }C$ is mixed with $10g$ of ice at $0^{\circ }C$. At equilibrium, the mixture contains $\frac{p}{q}$ gram of steam. Find $(p+q)$.

(Given: $s_{\text{water}}=1cal/g^{\circ }C,L_f=80cal/g,L_v=540cal/g$)

Q. In an experiment of measuring specific heat of a liquid, a stream of liquid flows at a steady rate of $5g/s$ over an electrical heater dissipating $135W$ and a temperature rise of $5K$ is observed. On increasing the rate of flow to $10g/s$, the same temperature rise is produced with a dissipation of $235W$. Find the specific heat $\left(J/gK\right)$ of the liquid. (Assume heat loss to the surrounding in both the cases is same.)

Q. A sample of an ideal gas has pressure $p_0$, volume $V_0$ and temperature $T_0$. It is isothermally expanded to twice its original volume. It is then compressed at constant pressure to have the original volume $V_0$. Finally, the gas is heated at constant volume to get the original temperature. The heat absorbed in the process is

1. $p_0{V}_0[\text{In}2+2]$
2. $p_0{V}_0[\text{In}2-\frac{1}{2}]$
3. $p_0{V}_0[\text{In}2+\frac{3}{2}]$
4. $p_0{V}_0[\text{In}2+\frac{1}{2}]$

Q. A piece of brass of volume $30~cm^3$ has a mass of $252~g.$ Fin the density of brass in $gcm^{-3}$.

Q. A calorimeter of mass $0.2kg$ and specific heat $900J/kg-K$. Containing $0.5kg$ of a liquid of specific heat $2400J/kg-K$. Its temperature falls from ${60}^{\circ }C$ to ${55}^{\circ }C$ in one minute. The rate of cooling is

1. $5j/s$
2. $100j/s$
3. $15j/s$
4. $115j/s$

Q.

In making an alloy, a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$; then the specific gravity of the alloy is

1. 

2. 

3. 

4. 

Q. The mass of a box measured by a grocer’s balance is $2.300kg$. Two gold pieces of masses $20.15g\text{and}20.17g$ are added to the box. What is
i) The Total mass of the box.
ii) The difference in the masses of the pieces to correct significant figures.

Q. Equal masses of two liquids having densities $d_1$ and $d_2$ are mixed together. The density of the resulting mixture is

1. $\frac{d_1+d_2}{2}$
2. $\frac{d_1-d_2}{d_1{d}_2}$
3. $\frac{d_1{d}_2}{d_1+d_2}$
4. $\frac{2d_1{d}_2}{d_1+d_2}$

Q. The correct formula for specific gravity of a substance is

1. $SG=\frac{\text{Density of substance}}{\text{Density of water at}{0}^{\circ }C}$
2. $SG=\frac{\text{Density of water}}{\text{Density of substance}}$
3. $SG=\frac{\text{Density of subtance}}{\text{Density of water at}{4}^{\circ }C}$
4. $SG=\frac{\text{Gravity force}}{\text{Mass}}$

Q. A sphere of mass $5\text{kg}$ and volume $2.2\times {10}^{-4}{\text{m}}^3$ is completely immersed in water. Find the buoyant force exerted by water on the sphere.

Density of water $=1000{\text{kg-m}}^{-3}$ and take $g=10{\text{m/s}}^2$

1. $2.1\text{N}$
2. $2.2\text{N}$
3. $2.4\text{N}$
4. $2.3\text{N}$

Q. How much steam at ${100}^{\circ }$ will just melt $64gm$ of ice at $-{10}^{\circ }C$?

Q. A mass of $1kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If the string $C$ is stretched slowly, then

1. None of the strings will break
2. The portion $BC$ of the string will break
   
3. None of the above
   
4. The portion $AB$ of the string will break
   

Q. When $0.4kg$ of water at ${30}^{\circ }C$ is mixed with $0.15kg$ of water at ${25}^{\circ }C$ contained in a calorimeter, the final temperature is found to be ${27}^{\circ }C$, find the water equivalent of the calorimeter.

1. $1kg$
2. $0.5kg$
3. $1.5kg$
4. $0.450kg$