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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?
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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| / |-
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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?
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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?.
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