Archimedes' Principle

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. A sample of metal weighs 210 gm in air, 180 gm in water and 120 gm in liquid. Then relative density (RD) of

1. Metal is 3
2. Metal is 7
3. Liquid is 3
4. Liquid is

Q.

A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?

1. It will slowly come back to its earlier position

2. It will remain floating where it was left

3. It will sink

4. It will come out violently

Q. The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is

1. 
2. 
3. 
4. None of these

Q. 12. A uniform cubical block is subjected to volumetriccompression, which decreases its each side by2% The Bulk strain produced in it is(1) 0.03(2) 0.02(4) 0.12(3) 0.06

Q. A large vessel of height H , is filled with a liquid of density P , up to the brim . A small hole of radius r is made at the side vertical face , close to the base . What is the horizontal force required to stop the gushing of liquid?

Q.

A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is

1. 1.6

2. 1.94

3. 3.1

4. 5.25

Q.

A block of steel of size 5 cm $\times$ 5 cm $\times$ 5 cm is weighed in water. If the relative density of steel is 7, its apparent weight is

1. 6 × 5 × 5 × 5 gf

2. 4 × 4 × 4 × 7 gf

3. 5 × 5 × 5 × 7 gf

4. 4 × 4 × 4 × 6 gf

Q. An ice cube contains a glass ball. The cube is floating on the surface of water contained in a trough. What will happen to the water level, when the cube melts?

1. It will fall

2. It will rise

3. It will remain unchanged

4. First it will fall and then rise

Q.

Force of viscosity acting on a spherical body of radius r moving with velocity v through a fluid of viscosity η is given by

1. F = 6 η r v

2. F = 6 π η r v

3. F = 6 η v/r

4. F = 6 π η v

Q. A solid of density D is floating in a liquid of density d. If v is the volume of solid submerged in the liquid and V is the total volume of the solid, then v/V equals to

1. 

2. 

3. 

4. 

Q. A small ball of density $\rho$ is immersed in a liquid of density $\sigma (>\rho )$ to a depth h and released. The height above the surface of water up to which the ball will jump is

1. $(\frac{\rho }{\sigma }-1)h$
2. $(\frac{\rho }{\sigma }-1)h$
3. $(\frac{\sigma }{\rho }-1)h$
4. $(\frac{\sigma }{\rho }+1)h$

Q. A hollow sphere which has a small hole in its bottom is immersed in water to a depth of 30 cm beforeany water enters in it. If the surface tension of water is 75 dynes/cm then find the radius of the hole inmetres (taking g-10 m/s?)

Q.

A man is carrying a block of a certain substance (of density 1000 kgm-3) weighing 1 kg in his left hand and a bucket filled with water and weighing 10 kg in his right hand. He drops the block into the bucket. How much load does he carry in his right hand now

1. 10 kg

2. 11 kg

3. 12 kg

4. 9 kg

Q.

A body of density d and volume V floats with volume $V_1$ of it immersed in a liquid of density $d_1$ and rest of the volume $V_2$ immersed in another liquid of density $d_2$(<$d_1$) then $V_1$ is

1. 

2. 

3. 

4. 

Q. A jet of liquid of cross sectional area a strikes a wall making angle θ with the wall.The water strikes with thw wall wirh velocity v and rebounds elastically.If density of liquid be ρ, tthe normal force on the wall is=?

Q. Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position
(a) $mg=\frac{m{v}^2}{r}$
(b) mg is greater than $\frac{m{v}^2}{r}$
(c) mg is not greater than $\frac{m{v}^2}{r}$
(d) mg is not less than $\frac{m{v}^2}{r}$.

Q. P27 A circular hole of radius r at the bottom of an initially full watercontainer is sealed by a ball of mass m and radius R. The depth of thewater is now slowly reduced, and when it reaches a certain value, ho the ballrises out of the hole. Find ho.

Q.

A body weighs $W_1$ in a liquid of density $d_1$ and $W_2$ in a liquid of density $d_2$. What is the weight in a liquid of density $d_3$?

1. 

2. 

3. 

4. 

Q. A small spherical object having density 2P is placed inside the liquid of density P and connected to an ideal string of length l whose other end is kept fixed so that the object can move in a vertical cirlcle, minimum speed which must be given at the bottom to just complete the vertical circle.

Q. A sphere of solid material of specific gravity $8$ has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must be

1. $\frac{7^{1/3}}{2}$
2. $\frac{5^{1/3}}{2}$
3. $\frac{9^{1/3}}{2}$
4. $\frac{3^{1/3}}{2}$

Q.

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3. For this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

1. 8

2. 4

3. 3

4. Zero

Q. What is the working process of a venturimeter ?

Q. 33.A small hollow sphere having a small hole in it , is immersed into water at a depth of 20cm before any water penetrates into it.If the surface tension of water is 73 dyne per cm, find the radius of the hole

Q. An uniform rod of density $\rho$ is placed in a wide tank containing a liquid of density ${\rho }_0({\rho }_0>\rho )$. The depth of the liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position, the rod makes an angle $\theta$ with the horizontal. Then, identify the correct relation :

1. $\sin \theta =\frac{1}{2}\sqrt{\frac{{\rho }_0}{\rho }}$
2. $\sin \theta =\frac{1}{2}\frac{{\rho }_0}{\rho }$
3. $\sin \theta =\sqrt{\frac{\rho }{{\rho }_0}}$
4. $\sin \theta =\frac{{\rho }_0}{\rho }$

Q. AN16) A slender homogeneous rod of length 2 L floats partly immersed in water being supported by a string fastenedto one of its end. The specific gravity of the rod is 0.75. The length of rod that extends out of water is 1 L 2 l/2 3 l/4 4 l/3

Q.

A sample of metal weighs 210 gm in air, 180 gm in water and 120 gm in liquid. Then relative density (RD) of

1. Metal is 7, Liquid is 3

2. Metal is 3, Liquid is 7

3. Metal is 4, Liquid is 9

4. Metal is 9, Liquid is 4

Q. 20.A large vessel of height H , is filled with a liquid of density P , up to the brim . A small hole of radius r is made at the side vertical face , close to the base . What is the horizontal force required to stop the gushing of liquid?

Q. A block of wood floats in water $\left(4/5\right)th$ of its volume submerged. If the same block just floats in a liquid, the density of liquid in ${\text{kg/m}}^3$ is
(Take density of water as $1000{\text{kg/m}}^3$)

1. $400{\text{kg/m}}^3$
2. $800{\text{kg/m}}^3$
3. $900{\text{kg/m}}^3$
4. $1250{\text{kg/m}}^3$

Q.

Describe briefly how you can show that the buoyant force acting on a solid body immersed in a liquid, does not depend on the nature of the solid body.