Advertisements
Advertisements
Question
A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. Water can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9.
Advertisements
Solution
Given:
Specific gravity of ice, ρice = 0.9 gm/cc
Weight of the metal piece, m = 500 g
Density of water, \[\rho_w\] = 103 kg/m3
Let x be the minimum edge of the ice block in cm.
We have:
mg + Wice = U
Here,
U = Upward thrust
Wice = Weight of the ice
\[\text{Thus, we have: }\]
\[0 . 5 \times \text{ g + x}^3 \times \rho_{\text{ ice }} \times \text{ g = x} ^3 \times \rho_w \times g \left[ \text{ Volume of the liquid displaced = x}^3 \right]\]
\[ \Rightarrow 0 . 5 \times {10}^3 + x^3 \times (0 . 9) = x^3 \times 1\]
\[ \Rightarrow x^3 \times (0 . 1) = (0 . 5) \times {10}^3 \]
\[ \Rightarrow x^3 = 5 \times {10}^3 \]
\[ \Rightarrow x = 17 . 09 \text{ cm}\]
\[ \Rightarrow x = 17 \text{ cm }\]
APPEARS IN
RELATED QUESTIONS
Derive an expression for excess pressure inside a drop of liquid.
A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 x 105 N/m2 ]
'n' droplets of equal size of radius r coalesce to form a bigger drop of radius R. The energy liberated is equal to...................
(T =Surface tension of water)
`(a) 4piR^2T[n^(1/3)-1]`
`(b) 4pir^2T[n^(1/3)-1]`
`(c) 4piR^2T[n^(2/3)-1]`
`(d)4 pir^2T[n^(2/3)-1]`
The surface tension of water at 0ºc is 75·5 dyne/cm. Find surface tension of water at 25°C. [ α for water = 0·0021/°C ]
In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass
of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a
vertical axis, calculate tension in the string (g = 9.8 m/s2)
A uniform vertical tube of circular cross section contains a liquid. The contact angle is 90°. Consider a diameter of the tube lying in the surface of the liquid. The surface to the right of this diameter pulls the surface on the left of it. What keeps the surface on the left in equilibrium?
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
Which of the following graphs may represent the relation between the capillary rise hand the radius r of the capillary?
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 Nm−1.
A metal piece of mass 160 g lies in equilibrium inside a glass of water. The piece touches the bottom of the glass at a small number of points. If the density of the metal is 8000 kg/m3, find the normal force exerted by the bottom of the glass on the metal piece.
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.
Derive an expression for capillary rise for a liquid having a concave meniscus.
Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7 × 10-2 N/m. The angle of contact between water and glass is zero, the density of water = 1000 kg/m3, g = 9.8 m/s2.
Distinguish between cohesive and adhesive forces.
The excess of pressure, due to surface tension, on a spherical liquid drop of radius 'R' is proportional to ______.
Soap solution is used for cleaning dirty clothes because ______.
What is surface tension? Explain the applications of surface tension.
Is surface tension a vector?
The excess pressure inside a liquid drop is 500 Nm-2. If the radius of the drop is 2 mm, the surface tension of the liquid is x × 10-3 Nm-1. The value of x is ______.
The surface tension of soap solution is 25 × 10-3 Nm-1. The excess of pressure inside a soap bubble of diameter 1 cm is ______.
