Buoyant Force

Q.

A uniformly tapering vessel is filled with a liquid of density 900 kg/$m^3$. The force that acts on the base of the vessel due to the liquid is $(g=10m{s}^{-2})$

1. 3.6 N

2. 7.2 N

3. 14.4 N

4. 9.0 N

Q. A clock with an iron pendulum keeps correct time at ${15}^{\circ }$C. What will be the error, in second per day, if the room temperature is ${20}^{\circ }$C? (The coefficient of linear expansion of iron is ${0.000012}^{\circ }{C}^{-1}$.)

1. 2.6 s
2. 6.2 s
3. 1.3 s
4. 3.1 s

Q. A wooden ball of density $D$ is immersed in water of density $d$ to a depth $h$ below the surface of water and then released. Upto what height will the ball jump out of water( measured from surface of water) ?

1. $\frac{d}{D}h$
2. $h$
3. $\text{Zero}$
4. $(\frac{d}{D}-1)h$

Q.

A cubical block of side $0.5\text{m}$ 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 under water?

[Take density of water $={10}^3{\text{kg/m}}^3$]

1. $46.3\text{kg}$
2. $30.1\text{kg}$
3. $87.5\text{kg}$
4. $65.4\text{kg}$

Q. Streamline flow is more likely for liquids with

1. high viscosity.
2. low density.
3. high density.
4. low viscosity.

Q. Which one of the following statements is true ?

1. Both light and sound waves in air are longitudinal.
2. Both light and sound waves in air are transverse.
3. Both light and sound waves can travel in vacuum.
4. The sound waves in air are longitudinal while the light waves are transverse.

Q. A simple pendulum oscillating in air has period $T$. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is ${\left(\frac{1}{16}\right)}^{th}$ of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

1. $4\text{T}\sqrt{\frac{1}{15}}$
2. $2\text{T}\sqrt{\frac{1}{10}}$
3. $4\text{T}\sqrt{\frac{1}{14}}$
4. $2\text{T}\sqrt{\frac{1}{14}}$

Q. A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is

1. Zero
2. Equal to the weight of the liquid displaced
3. Equal to the weight of the body in air
4. Equal to the weight of the immersed position of the body

Q. Three masses, each equal to $M$, are placed at the three corners of a square of side $a$. The force of attraction on unit mass at the fourth corner will be

1. $\frac{GM}{a^2}\sqrt{3}$
2. $\frac{GM}{3a^2}$
3. $\frac{GM}{a^2}[\frac{1}{2}+\sqrt{2}]$
4. $\frac{3GM}{a^2}$

Q.

A fluid is flowing through a horizontal pipe of varying cross-section, with speed$vm{s}^{-1}$ at a point where the pressure is $Ppascal$. At another point where pressure is $P/2pascal$ its speed is $Vm{s}^{-1}$. If the density of the fluid is $\rho$ in $kg{m}^{-3}$ and the flow is streamlined, then $V$ is equal to:

1. $\sqrt{\left[\right(P/2\rho )+v^2]}$

2. $\sqrt{\left[\right(P/\rho )+v^2]}$

3. $\sqrt{\left[\right(2P/\rho )+v^2]}$

4. $\sqrt{\left[\right(P/\rho )+v]}$

Q.

Water flows through a tube shown in figure. The areas of cross section at A and B are 1 $c{m}^2$ and 0.5 $c{m}^2$ respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm $s^{-}1$, find (a) the speed at B and (b) the difference in pressures at A and B.

Q. A cubical metal block of edge $12\text{cm}$ floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is immersed in it. Height of the water column to be poured is [specific gravity of mercury$=13.6$]

1. $10.4\text{cm}$
2. $8.4\text{cm}$
3. $6.4\text{cm}$
4. $5.4\text{cm}$

Q. A metallic sphere of mass $3\text{kg}$ is held by a string and is completely immersed in a liquid of relative density $0.8$. The relative density of the metallic sphere is $10$. What is the tension in the string?
Take $g=10{\text{ms}}^{-1}$

1. $18.7\text{N}$
2. $27.6\text{N}$
3. $42.5\text{N}$
4. $32.7\text{N}$

Q. A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid. If the whole of the system accelerates upwards with acceleration $g/4$, the fraction of volume immersed in the liquid will be

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

Q.

In a simple Atwood machine, two unequal masses $m_1$ and $m_2$ are connected by a string going over a clamped light smooth pulley. In a typical arrangement (Figure) $m_1=300$ g and $m_2=600$g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds. (b) Find the tension in the string. (c) Find the force exerted by the clamp on the pulley.

Q. A simple pendulum has a time period $T$ in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of the material of the bob is

1. $\sqrt{\frac{7}{8}}T$
2. $\sqrt{\frac{5}{8}}T$
3. $\sqrt{\frac{3}{8}}T$
4. $\sqrt{\frac{8}{7}}T$

Q. A simple pendulum with a solid metal bob has time period $T$. The metal bob is now completely immersed in a liquid of density one-tenth that of the bob. The liquid is non-viscous. Now the period of the same pendulum, remaining all the time immersed in the liquid, will be,

1. $T$
2. $\left(\frac{9}{10}\right)T$
3. $T\sqrt{\frac{10}{9}}$
4. $\sqrt{\frac{9T}{10}}$

Q. If in a system the force of attraction between two-point masses of $1kg$ each situated $1km$ apart is taken as a unit force and is called notwen (newton written in reverse order) and if $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$ in SI units, the relation of notwen and newton is:

1. $1\text{notwen}=6.67\times {10}^{-11}\text{newton}$
2. $1\text{notwen}=6.67\times {10}^{-19}\text{newton}$
3. $1\text{notwen}=6.67\times {10}^{-12}\text{newton}$
4. $1\text{notwen}=6.67\times {10}^{-17}\text{newton}$

Q. Find the density of a metallic body which floats at the interface of mercury of specific gravity $13.6$ and water such that $31.75\%$ of its volume is submerged in mercury and $68.25\%$ in water.

1. $6000{\text{kg/m}}^3$
2. $5000{\text{kg/m}}^3$
3. $4000{\text{kg/m}}^3$
4. $7000{\text{kg/m}}^3$

Q. Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$, respectively, are released in free space with initial separation between their centres equal to $12R$. If they attract each other due to the gravitational force only, then the distance covered by the smaller body just before collision is

1. $7.5R$
2. $7R$
3. $6R$
4. $8.5R$

Q.

The sound carried by air from a sitar to a listener is a wave of which of the following type:

1. Longitudinal stationary

2. Transverse progressive

3. Transverse stationary

4. Longitudinal progressive

Q. Six-point masses of mass $m$ each are at the vertices of a regular hexagon of side $l$. Calculate the force on any of the masses.

Q. Ratio of the weights of a $1\text{kg}$ block of iron and $1\text{kg}$ block of wood as measured by a spring balance is:
Given: Density of iron $=7800{\text{kg/m}}^3$, density of wood $=800{\text{kg/m}}^3$ and density of air $=1.293{\text{kg/m}}^3$

1. $1.5$
2. $2.0015$
3. $1.0015$
4. $3.0015$

Q. If $R_E$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth $r$ below and a height $r$ above the earth surface is (Given $r<R_E$)

1. $1+\frac{r}{R_E}+\frac{r^2}{R_E^2}+\frac{r^3}{R_E^3}$
2. $1+\frac{r}{R_E}-\frac{r^2}{R_E^2}-\frac{r^3}{R_E^3}$
3. $1-\frac{r}{R_E}-\frac{r^2}{R_E^2}-\frac{r^3}{R_E^3}$
4. $1+\frac{r}{R_E}-\frac{r^2}{R_E^2}+\frac{r^3}{R_E^3}$

Q.

A $5.5metre$length of the string has a mass of $0.035kg$. if the tension in the string is $77N$, the speed of a wave on the string is

1. $110m{s}^{-1}$

2. $165m{s}^{-1}$

3. $77m{s}^{-1}$

4. $102m{s}^{-1}$

Q. A uniform rod $\text{AB},4\text{m}$ long and weight $12\text{kg}$, is supported at end A, with a $6\text{kg}$ lead weight at B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total volume of the rod.

1. $10\text{N},32\times {10}^{-3}{\text{m}}^3$
2. $20\text{N},32\times {10}^{-3}{\text{m}}^3$
3. $20\text{N},16\times {10}^{-3}{\text{m}}^3$
4. $10\text{N},16\times {10}^{-3}{\text{m}}^3$

Q. A metal ball weighs $0.096\text{N}$ in air. If suspended in water, it has an apparent weight of $0.071\text{N}$. The density of the metal ball is

1. $3840{\text{kg/m}}^3$
2. $2040{\text{kg/m}}^3$
3. $2540{\text{kg/m}}^3$
4. $4838{\text{kg/m}}^3$

Q. A uniform rod $AB,12\text{m}$ long and weighing $24\text{kg}$, is supported at end $B$ by a flexible light string and a lead mass (of very small size) of $12\text{kg}$ is attached at end $A$. The rod floats in water with half of its length submerged. For the situation described, choose the correct statement(s). [Take $g=10{\text{m/s}}^2$, density of water $=1000{\text{kg/m}}^3$]

1. The tension in the string is $40\text{N}$.
2. The tension in the string is $120\text{N}$.
3. The volume of the rod is $6.4\times {10}^{-2}{\text{m}}^3$.
4. The point of action of the buoyant force is $C$ (centre of mass of rod).

Q.

Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1 mm. find the rise of water in the space between the plates. Surface tension of water = 0.075 N m^-1.

1. 1.5 mm

2. 15 cm

3. 1.5 cm

4. 0.015 cm

Q. A $20\text{N}$ metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads $40\text{N}$. The spring balance is now lowered slowly into the beaker such that the block gets immersed in the water. The spring balance now reads $16\text{N}$. The reading of the weighing machine will be

1. $36\text{N}$
2. $60\text{N}$
3. $44\text{N}$
4. $56\text{N}$