Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Angle of contact for the pair of pure water with clean glass is _______.
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 ]
Explain why Surface tension of a liquid is independent of the area of the surface
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.
The contact angle between water and glass is 0°. When water is poured in a glass to the maximum of its capacity, the water surface is convex upward. The angle of contact in such a situation is more than 90°. Explain.
Which of the following graphs may represent the relation between the capillary rise hand the radius r of the capillary?
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.
A 5.0 cm long straight piece of thread is kept on the surface of water. Find the force with which the surface on one side of the thread pulls it. Surface tension of water = 0.076 N m−1.
The lower end of a capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, up to what height will the water rise in the capillary?
A barometer is constructed with its tube having radius 1.0 mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to 76 cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass = 135° and surface tension of mercury = 0.465 N m−1. Density of mercury = 13600 kg m−3.
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.
A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.
A solid sphere of radius 5 cm floats in water. If a maximum load of 0.1 kg can be put on it without wetting the load, find the specific gravity of the material of the sphere.
The water droplets are spherical in free fall due to ______
Obtain an expression for the capillary rise or fall using the forces method.
How does the friction arise between the surfaces of two bodies in relative motion?
Explain elasticity using intermolecular forces.
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]
Why is raindrop spherical in nature?
In a U-tube, the radii of two columns are respectively r1 and r2. When a liquid of density ρ(θ = 0°) is filled in it, a level difference of h is observed on two arms, then the surface tension of the liquid is ______.
