Advertisements
Advertisements
प्रश्न
A cubical block of wood weighing 200 g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3.
Advertisements
उत्तर
Given:
Density of wood, ρw = 0.8 gm/cc
Density of lead, ρpb = 11.3 gm/cc
Weight of the cubical wood block, mw = 200 g
The cubical block floats in water.
Now,
(mw+ mpb) × g = (Vw + Vpb)ρ × g
Here,
ρ = Density of water
Vw = Volume of wood
Vpb = Volume of lead
\[\Rightarrow ( \text{m}_\text{w} + \text{m}_{\text{pb}} ) = \left( \frac{\text{m}_\text{w}}{\rho_\text{w}} + \frac{\text{ m}_{\text{pb}}}{\rho_{\text{pb}}} \right)\rho\]
\[ \Rightarrow (200 + \text{m}_{\text{pb}} ) = \left( \frac{200}{0 . 8} + \frac{\text{m}_{\text{pb}}}{11 . 3} \right) \times 1\]
\[ \Rightarrow \text{m}_{\text{pb}} - \frac{\text{m}_{\text{pb}}}{11 . 3} = 250 - 200\]
\[ \Rightarrow \frac{10 . 3 \text{m}_{\text{pb}}}{11 . 3} = 50\]
\[ \Rightarrow \text{m}_{\text{pb}} = \frac{50 \times 11 . 3}{10 . 3} = 54 . 8 \text{ gm }\]
APPEARS IN
संबंधित प्रश्न
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.
Figure (a) shows a thin liquid film supporting a small weight = 4.5 × 10–2 N. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c)? Explain your answer physically.
What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 × 10–2 N m–1? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is 1.01 × 105 Pa).
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
State any two characteristics of the angle of contact
If water in one flask and castor oil in other are violently shaken and kept on a table, which will come to rest earlier?
The properties of a surface are different from those of the bulk liquid because the surface molecules
(a) are smaller than other molecules
(b) acquire charge due to collision from air molecules
(c) find different type of molecules in their range of influence
(d) feel a net force in one direction.
Find the force exerted by the water on a 2 m2 plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?
A cubical metal block of edge 12 cm floats in mercury with one fifth of the height inside the mercury. Water in it. Find the height of the water column to be poured.
Specific gravity of mercury = 13.6.
Define surface tension.
Obtain an expression for the capillary rise or fall using the forces method.
A capillary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `(2/3)` of its previous value, then compute the height up to which water will rise in the new capillary?
Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be ______.
Water rises upto a height h in a capillary tube on the surface of the earth. The value of h will increase, if the experimental setup is kept in [g = acceleration due to gravity]
A molecule of water on the surface experiences a net ______.
Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10–3 Nm–1.
A liquid drop of density ρ is floating half immersed in a liquid of density d. The diameter of the liquid drop is ______.
(ρ > d, g = acceleration due to gravity, T = surface tension)
Find the work done when a drop of mercury of radius 2 mm breaks into 8 equal droplets. [Surface tension of mercury = 0.4855 J/m2].
A drop of water of radius 8 mm breaks into number of droplets each of radius 1 mm. How many droplets will be formed?
