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Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg?
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Two masses 800kg and 600kg are at a distance of 0.25m apart compute th...
Solutio
hence
Let EA be the gravitational field intensity at point P due to 800 kg sphere at A.
Then, EA = G 800/(0.2)2 = 2 x 104 along PA
Let EB be the gravitational field intensity at P due yo 600 kg sphere at B
Then, EB = G 600/(0.15)2 = 80000G/3 along PB
The angle between EA and EB is 90°. [•.• AB2 = AP2 + BP2 ]
If E be the magnitude of the resultant intensity, then
E = √(EA2 + EB2)
= √(2 x 104 G)2 + (80000G/3)2
=G √4 x 108 + 64/9 x 108
= 6.67 x 10-11 x 2 x 104 √1 + 16/9
= 6.67 x 2 x 5/3 x 10-7 N kg-1
E = 2.22 x 10-6 N kg-1
Resultant force on
body at
is,
hence
Let EA be the gravitational field intensity at point P due to 800 kg sphere at A.
Then, EA = G 800/(0.2)2 = 2 x 104 along PA
Let EB be the gravitational field intensity at P due yo 600 kg sphere at B
Then, EB = G 600/(0.15)2 = 80000G/3 along PB
The angle between EA and EB is 90°. [•.• AB2 = AP2 + BP2 ]
If E be the magnitude of the resultant intensity, then
E = √(EA2 + EB2)
= √(2 x 104 G)2 + (80000G/3)2
=G √4 x 108 + 64/9 x 108
= 6.67 x 10-11 x 2 x 104 √1 + 16/9
= 6.67 x 2 x 5/3 x 10-7 N kg-1
E = 2.22 x 10-6 N kg-1
Resultant force on
body at
is,
Community Answer
Two masses 800kg and 600kg are at a distance of 0.25m apart compute th...
**Calculation of gravitational field intensity at the given point**
To calculate the magnitude of the gravitational field intensity at the given point, we need to use the formula for gravitational field intensity:
E = G * (m1 / r1^2 + m2 / r2^2)
Where:
E is the gravitational field intensity,
G is the universal gravitational constant (6.67 x 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the objects, and
r1 and r2 are the distances between the point and the masses.
**Calculating the gravitational field intensity due to the 800kg mass**
Given:
Mass of the 800kg object (m1) = 800kg
Distance from the point to the 800kg mass (r1) = 0.20m
Using the formula, we substitute the values:
E1 = G * (m1 / r1^2)
= (6.67 x 10^-11 Nm^2/kg^2) * (800kg / (0.20m)^2)
= (6.67 x 10^-11) * (800 / 0.04)
= (6.67 x 10^-11) * 20000
= 1.334 x 10^-6 N/kg
**Calculating the gravitational field intensity due to the 600kg mass**
Given:
Mass of the 600kg object (m2) = 600kg
Distance from the point to the 600kg mass (r2) = 0.15m
Using the formula, we substitute the values:
E2 = G * (m2 / r2^2)
= (6.67 x 10^-11 Nm^2/kg^2) * (600kg / (0.15m)^2)
= (6.67 x 10^-11) * (600 / 0.0225)
= (6.67 x 10^-11) * 26666.6667
= 1.777 x 10^-6 N/kg
**Calculating the net gravitational field intensity**
To find the net gravitational field intensity at the given point, we add the individual field intensities due to each mass:
E_total = E1 + E2
= 1.334 x 10^-6 N/kg + 1.777 x 10^-6 N/kg
= 3.111 x 10^-6 N/kg
Therefore, the magnitude of the gravitational field intensity at the given point is 3.111 x 10^-6 N/kg.
To calculate the magnitude of the gravitational field intensity at the given point, we need to use the formula for gravitational field intensity:
E = G * (m1 / r1^2 + m2 / r2^2)
Where:
E is the gravitational field intensity,
G is the universal gravitational constant (6.67 x 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the objects, and
r1 and r2 are the distances between the point and the masses.
**Calculating the gravitational field intensity due to the 800kg mass**
Given:
Mass of the 800kg object (m1) = 800kg
Distance from the point to the 800kg mass (r1) = 0.20m
Using the formula, we substitute the values:
E1 = G * (m1 / r1^2)
= (6.67 x 10^-11 Nm^2/kg^2) * (800kg / (0.20m)^2)
= (6.67 x 10^-11) * (800 / 0.04)
= (6.67 x 10^-11) * 20000
= 1.334 x 10^-6 N/kg
**Calculating the gravitational field intensity due to the 600kg mass**
Given:
Mass of the 600kg object (m2) = 600kg
Distance from the point to the 600kg mass (r2) = 0.15m
Using the formula, we substitute the values:
E2 = G * (m2 / r2^2)
= (6.67 x 10^-11 Nm^2/kg^2) * (600kg / (0.15m)^2)
= (6.67 x 10^-11) * (600 / 0.0225)
= (6.67 x 10^-11) * 26666.6667
= 1.777 x 10^-6 N/kg
**Calculating the net gravitational field intensity**
To find the net gravitational field intensity at the given point, we add the individual field intensities due to each mass:
E_total = E1 + E2
= 1.334 x 10^-6 N/kg + 1.777 x 10^-6 N/kg
= 3.111 x 10^-6 N/kg
Therefore, the magnitude of the gravitational field intensity at the given point is 3.111 x 10^-6 N/kg.
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Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg?
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Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg?.
Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses 800kg and 600kg are at a distance of 0.25m apart compute the magnitude of intensity of the gravitational field at a point distance 0.20m to from 800kg and 0.15 m from 600kg?.
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