Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:
Radius of the sphere, r = 5 cm
Mass of the maximum load, m = 0.1 kg
Let the weight of the sphere be W1 and the weight of the load be W2.
Now,
W1 + W2 = U
Here, U is the upward thrust.
Let V be the volume of the sphere.
\[\text{ Thus, we have: } \]
\[\text{mg + V }\times \rho_\text{s} \times \text{g = v } \times \rho_\text{w } \times \text{g}\]
\[\text{Here, }\]
\[ \rho_\text{ s }=\text{ Density of the sphere in gm/cc }\]
\[ \rho_\text{w }=\text{ Density of water }\]
\[\text{ On substituting the respective values in the above equation, we get: } \]
\[ (0 . 1) \times {10}^3 + \left( \frac{4}{3} \right) \times \pi \times (5 )^3 \times \rho_s = \left( \frac{4}{3} \right) \times \pi \times (5 )^3 \times 1\]
\[ \Rightarrow 100 = \left( \frac{4}{3} \right) \times \pi \times 125 \times (1 - \rho_\text{s} )\]
\[ \Rightarrow 1 - \rho_\text{s} = \frac{3 \times 100}{4 \times \pi \times 125} = 0 . 19\]
\[ \Rightarrow \rho_\text{s} = 1 - (0 . 19)\]
\[ = 0 . 81 \text{ gm/cc = 0 . 8 gm/cc}\]
APPEARS IN
RELATED QUESTIONS
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.
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
When a sparingly soluble substance like alcohol is dissolved in water, surface tension of water
If two soap bubbles of different radii are connected by a tube,
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.
When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary.
(a) The surface tension of the liquid must be zero.
(b) The contact angle must be 90°.
(c) The surface tension may be zero.
(d) The contact angle may be 90°.
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.
What will be the shape of the liquid meniscus for the obtuse angle of contact?
Water rises to a height of 20 mm in a capillary tube. If the radius made 1/3rd of its previous value, to what height will the water now rise in the tube?
How does surface tension help a plant?
The wettability of a surface by a liquid depends primarily on
What is capillarity?
Obtain an expression for the surface tension of a liquid by the capillary rise method.
A spherical soap bubble A of radius 2 cm is formed inside another bubble B of radius 4 cm. Show that the radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lesser than the radius of both soap bubbles A and B.
Why coffee runs up into a sugar lump (a small cube of sugar) when one corner of the sugar lump is held in the liquid?
The wear and tear in the machine part is due to ______.
The length of a needle floating on water is 2 cm. The additional force due to surface tension required to pull the needle out of water will be (S.T. of water = 7.0 × 10−2 N/m).
Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.
A soap film of surface tension 3 × 10-2 formed in a rectangular frame can support a straw as shown in Fig. If g = 10 ms-12, the mass of the straw is ______.
