Class 11 Exam  >  Class 11 Questions  >  A hollow cone floats with its axis vertical u... Start Learning for Free
A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given by
  • a)
    1.0
  • b)
    1.5
  • c)
    2.1
  • d)
    1.9
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
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
1​g=V×800×g/27​..(1) ,Volume of cone with height is h/3 is V/27
1​g+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
Most Upvoted Answer
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).
Attention Class 11 Students!
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.
Explore Courses for Class 11 exam

Top Courses for Class 11

A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer?
Question Description
A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer?.
Solutions for A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density r is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is 0.10 m and radius of the circular base is 0.05 m. The specific gravity r is given bya)1.0b)1.5c)2.1d)1.9Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam

Top Courses for Class 11

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev