NEET Exam > NEET Questions > Two solid uniform spheres each of radius 5 cm...
Start Learning for Free
Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4?
Most Upvoted Answer
Two solid uniform spheres each of radius 5 cm are connected by a light...
Given:
- Radius of each sphere: 5 cm
- Specific gravity of first sphere: 0.5
- Specific gravity of second sphere: 2
To find:
- Ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere
Solution:
Step 1: Calculate the mass of each sphere
The mass of a sphere can be calculated using the formula:
Mass = (4/3) x π x r^3 x density
Given that the radius of each sphere is 5 cm, we can calculate the mass of each sphere as follows:
- Mass of the first sphere:
Density of water = 1 g/cm^3
Density of the first sphere = specific gravity x density of water = 0.5 x 1 = 0.5 g/cm^3
Mass of the first sphere = (4/3) x π x (5^3) x 0.5 = 125 x 0.5 x π = 62.5π g
- Mass of the second sphere:
Density of the second sphere = specific gravity x density of water = 2 x 1 = 2 g/cm^3
Mass of the second sphere = (4/3) x π x (5^3) x 2 = 250 x 2 x π = 500π g
Step 2: Calculate the weight of each sphere
The weight of a sphere can be calculated using the formula:
Weight = Mass x Gravitational acceleration
Given that the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight of each sphere as follows:
- Weight of the first sphere:
Weight of the first sphere = Mass of the first sphere x Gravitational acceleration = 62.5π x 9.8 = 612.5π N
- Weight of the second sphere:
Weight of the second sphere = Mass of the second sphere x Gravitational acceleration = 500π x 9.8 = 4900π N
Step 3: Calculate the tension in the string
Since the spheres are connected by a light string, the tension in the string will be the same for both spheres. Therefore, the tension in the string can be calculated as the sum of the weights of the two spheres:
Tension in the string = Weight of the first sphere + Weight of the second sphere
Tension in the string = 612.5π + 4900π = 5512.5π N
Step 4: Calculate the contact force between the bottom of the tank and the heavier sphere
The contact force between the bottom of the tank and the heavier sphere can be calculated as the difference between the weight of the heavier sphere and the tension in the string:
Contact force = Weight of the second sphere - Tension in the string
Contact force = 4900π - 5512.5π = -612.5π N
Step 5: Calculate the ratio of tension in the string and the contact force
Ratio of tension in the string and the contact force = |Tension in the string| / |Contact force|
Ratio of tension in the string and the contact force = |5512.5π| / |-
- Radius of each sphere: 5 cm
- Specific gravity of first sphere: 0.5
- Specific gravity of second sphere: 2
To find:
- Ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere
Solution:
Step 1: Calculate the mass of each sphere
The mass of a sphere can be calculated using the formula:
Mass = (4/3) x π x r^3 x density
Given that the radius of each sphere is 5 cm, we can calculate the mass of each sphere as follows:
- Mass of the first sphere:
Density of water = 1 g/cm^3
Density of the first sphere = specific gravity x density of water = 0.5 x 1 = 0.5 g/cm^3
Mass of the first sphere = (4/3) x π x (5^3) x 0.5 = 125 x 0.5 x π = 62.5π g
- Mass of the second sphere:
Density of the second sphere = specific gravity x density of water = 2 x 1 = 2 g/cm^3
Mass of the second sphere = (4/3) x π x (5^3) x 2 = 250 x 2 x π = 500π g
Step 2: Calculate the weight of each sphere
The weight of a sphere can be calculated using the formula:
Weight = Mass x Gravitational acceleration
Given that the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight of each sphere as follows:
- Weight of the first sphere:
Weight of the first sphere = Mass of the first sphere x Gravitational acceleration = 62.5π x 9.8 = 612.5π N
- Weight of the second sphere:
Weight of the second sphere = Mass of the second sphere x Gravitational acceleration = 500π x 9.8 = 4900π N
Step 3: Calculate the tension in the string
Since the spheres are connected by a light string, the tension in the string will be the same for both spheres. Therefore, the tension in the string can be calculated as the sum of the weights of the two spheres:
Tension in the string = Weight of the first sphere + Weight of the second sphere
Tension in the string = 612.5π + 4900π = 5512.5π N
Step 4: Calculate the contact force between the bottom of the tank and the heavier sphere
The contact force between the bottom of the tank and the heavier sphere can be calculated as the difference between the weight of the heavier sphere and the tension in the string:
Contact force = Weight of the second sphere - Tension in the string
Contact force = 4900π - 5512.5π = -612.5π N
Step 5: Calculate the ratio of tension in the string and the contact force
Ratio of tension in the string and the contact force = |Tension in the string| / |Contact force|
Ratio of tension in the string and the contact force = |5512.5π| / |-
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4?
Question Description
Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4?.
Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4?.
Solutions for Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? defined & explained in the simplest way possible. Besides giving the explanation of
Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4?, a detailed solution for Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? has been provided alongside types of Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? theory, EduRev gives you an
ample number of questions to practice Two solid uniform spheres each of radius 5 cm are connected by a light string and totally immersed in a tank of water. If the specific gravities of the sphere are 0.5 and 2. Find the ratio of tension in the string and the contact force between the bottom of the tank and the heavier sphere. a. 1:1 b. 1:2 c. 1:3 d. 1:4? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup