Buoyant Force

Q.

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be

1. 1/2

2. 3/8

3. 2/3

4. 3/4

Q.

A glass full of water has a bottom of area 20 cm², top of area 20 cm², height 20 cm and volume half a liter. Considering the equilibrium of the water, find the resultant force exerted by the sides of the glass on water. Atmospheric pressure = 105 N/m², density of water = 1000 kg/m³ and g = 10 m/s².

1. 204 N upwards

2. 205 N upwards

3. 1 N upwards

4. 205 N downwards

Q. A solid sphere of density $\eta (>1)$ times lighter than that of water is suspended in a water tank by a string tied to its base as shown in figure. If the mass of the sphere is $m$, then the tension in the string is given by

1. $\left(\frac{\eta -1}{\eta }\right)$
2. $\eta mg$
3. $\frac{mg}{\eta -1}$
4. $(\eta -1)mg$

Q. An iceberg is floating in sea water. The density of ice is $0.92gm/c{m}^3$ and that of sea water is $1.03gm/c{m}^3$. What percentage of the iceberg will be below the surface of water

1. 
2. 
3. 
4. 

Q.

A metallic block of density 5 gm $c{m}^{-3}$ and having dimensions 5 cm $\times$ 5 cm $\times$ 5 cm is weighed in water. Its apparent weight will be

1. 4 × 4 × 4 × 4 gf

2. 5 × 5 × 5 × 5 gf

3. 5 × 4 × 4 × 4 gf

4. 4 × 5 × 5 × 5 gf

Q. If a composite physical quantity in terms of moment of inertia \((I)\), force \((F)\), velocity \((v)\), work \((W)\) and length \((L)\) is defined as \(Q=\dfrac{IFv^2}{WL^3}\), then \(Q\) may be

Q. The density of a wooden block is 0.8 g/cm3. The percentage by volume of the block immersed in the water is

Q. 25, A ball of density and radius r is dropped on thesurface of a liquid of density p from certain height, ifspeed of ball does not change even on entering inliquid and viscosity of liquid is η , then the heightfrom which ball dropped is2 , 29η 2(o-p)r(3)--9η (4) 2g9η

Q. in a human pyramid in a circus , the entire weight of the balanced roup is supported by the legs of a performer wo is lying on his back. the combined mass of all the persons performing the act, and the tables, palques etc involved is 280kg . the mass of the performer lying on his back at the bottom of the pyramid is 60kg. each thigh bone of this performer has a lenght of 50cm and effevtive radius of 2 cm . determine the amount by which each thigh bone gets compressed under the extra load.

Q. Water drop of radius 1.5 mm is falling from height 1 km having drag constant .5 density of water drop 1000 kg per metre cube and density of air is 1.29 kg per metre cube find its terminal velocity

Q.

A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring

1. Increases

2. Decreases

3. Remains unchanged

4. None of these

Q. An incompressible liquid of density p is enclosedwith two frictionless pistons one of cross-sectionalarea A and the other of 4A. When the narrowpiston moves in by a distance h, the wider pistonmoves out by a distance.(2) 4h(1) hh(3)(4) 54

Q.

A fisherman hooks an old log of wood of weight 12N and volume 1000 $c{m}^3$. He pulls the log half way out of water. The tension in the string at this instant is

1. 8 N

2. 10 N

3. 7 N

4. 12 N

Q. If a composite physical quantity in terms of moment of inertia $\left(I\right)$, force $\left(F\right)$, velocity $\left(v\right)$, work $\left(W\right)$ and length $\left(L\right)$ is defined as $Q=\frac{IF{v}^2}{W{L}^3}$, then $Q$ may be

1. Surface tension
2. Both (a) and (b)
3. None of these
4. Surface energy

Q. 19. The density of ice is 0.9g/c and that of sea water is 1.1g/cc . An iceberg of volume V is floating in sea water. The fraction of iceberg above water level is

Q. 4. 12. A : Buoyant force is always vertically upward. R : Buoyant force is always opposite to the direction of acceleration due to gravity.

Q. A uniform cubical block of density ${\rho }_b\left(\text{in g/cc}\right)$ and length a is released from rest from the position where one of its horizontal surface (lower) just touches the water (density ${\rho }_w=1\text{g/cc}$). The time period of oscillation of the block is $({\rho }_b=\frac{2}{3}\text{g/cc},\text{neglect viscosity and surface tension})$

1. $2\pi \sqrt{\frac{p_{b}a}{p_{w}g}}$
2. $2\pi \sqrt{\frac{p_{w}a}{p_{b}g}}$
3. $\frac{4\pi }{3}\sqrt{\frac{p_{b}a}{p_{w}g}}+\frac{p_b}{p_w-p_b}\sqrt{\frac{4p_{w}a}{3p_{b}g}}$
4. $\frac{2\pi }{3}\sqrt{\frac{p_{b}a}{p_{w}g}}+\frac{p_b}{p_w-p_b}\sqrt{\frac{2p_{w}a}{3p_{b}g}}$

Q. 36. A block is partially immersed in liquid and vessel containing the liquid is moving upward with an acceleration a. The block is observed by two observers O1 and O2, O1 at rest and O2 is moving upward with an acceleration a. Find the total upward buoyant force on the block.

Q. Two solid metal balls of radii r and 2r are falling with their terminal speeds in a viscous liquid what is the ratio of drag force acting on these two balls

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. TWO RAIN DROPS OF WATER REACH THE EARTH SURFACE WITH THE TERMINAL VELOCITY IN THE RATIO OF 4:9 . THE RATIO OF THEIR MASSES WILL BE

Q. An engine pumps a fluid of density 1200 kg/m3through a tube of crosS-section area of 4 cm2through a height of 5 m with a speed of 40 cm/sFind the power of engine.

Q.

A U-tube contains water and oil separated by mercury. The mercury columns in the two arms are at the same level with 10 cm of water in one arm and 12.5 cm of oil in the other, as shown in the figure. What is the relative density of oil?

1. 0.8

2. 1.0

3. 1.2

4. 1.4

Q. is critical velocity of liquid is inversely proportional to the radius of the tube

Q.

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be

1. 1/2

2. 3/8

3. 2/3

4. 3/4

Q. A stone is dropped from the roof of a tower of height h. the total distance covered by the stone in the last 2 seconds of its motion is equal to distance covered by it in first four seconds. find the height of the tower.

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 bodies are in equilibrium when suspended in water from the arm of a balance. The mass of one body is 60g and its density is 12g/cc.If the mass of the other body is 72g , then its density in g/cc

Q.

A log of wood of mass 120 Kg floats in water. The weight that can be put on the raft to make it just sink should be (density of wood=600Kg/m³)

1. 80 Kg

2. 50 Kg

3. 60 Kg

4. 30 Kg

Q. Weight of a body decreases by 1.5%, when it is raised to a height h above the surface of earth. When the same body is taken to some depth h in a mine, its weight will show 1) 0.75% increase 2) 3.0% decrease 3) 0.75% decrease 4) 1.5% decrease