A hollow cone floats with its axis vertical upto one-third of its heig...
Let the volume of cylinder be V and density to be ρ1
Vρ1g=V×800×g/27..(1) ,Volume of cone with height is h/3 is V/27
Vρ1g+Vρg/27=V×800g/8 ..(2) ,Volume of cone with height is h/2 is V/8
from above equation we ρ=800×19/8
Specific gravity =1900/1000=1.9
View all questions of this test
A hollow cone floats with its axis vertical upto one-third of its heig...
Given data:
Height of the cone (h) = 0.10 m
Radius of the circular base (r) = 0.05 m
Relative density of the first liquid (ρ1) = 0.8
Let's consider the first case where the cone is floating in the first liquid:
Height of the cone submerged in the first liquid (h1) = h/3 = 0.10/3 = 0.0333 m
Volume of the cone submerged in the first liquid (V1) = (1/3)πr²h1
Buoyant force acting on the cone in the first liquid (Fb1) = V1ρ1g, where g is the acceleration due to gravity
Weight of the cone (W) = mg = ρgV, where ρ is the density of the material of the cone and V is its volume
For the cone to float, Buoyant force = Weight of the cone
Therefore, V1ρ1g = ρgV
Simplifying the equation, we get,
V1/V = 1/ρ1
Substituting the given values, we get,
V1/V = 1/0.8
V1/V = 1.25
Let's consider the second case where the cone is floating in the second liquid:
Height of the cone submerged in the second liquid (h2) = h/2 = 0.10/2 = 0.05 m
Volume of the cone submerged in the second liquid (V2) = (1/3)πr²h2
Buoyant force acting on the cone in the second liquid (Fb2) = V2ρg, where ρ is the relative density of the second liquid
For the cone to float, Buoyant force = Weight of the cone
Therefore, V2ρg = ρgV
Simplifying the equation, we get,
V2/V = 1/ρ
Substituting the given values, we get,
V2/V = 2
Equating the values of V1/V and V2/V, we get,
1.25 = 2/ρ
Solving for ρ, we get,
ρ = 2/1.25
ρ = 1.6
Since the question asks for the specific gravity of the second liquid, we need to divide the relative density by the density of water (1000 kg/m³) to get the specific gravity,
Specific gravity = Relative density/density of water
Specific gravity = 1.6/1000
Specific gravity = 0.0016
Converting the specific gravity to the required format (multiply by 1000 and round off to one decimal place), we get,
Specific gravity = 1.6
Therefore, the correct answer is option D (1.9 is not the correct answer).
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.