Effect of the Earth's Shape on g: The Earth is not a perfect sphere; it is slightly flattened at the poles and bulges at the equator. This means the equatorial radius of the Earth is about 21 km greater than the polar radius. Since the acceleration due to gravity is inversely proportional to the squRead more
Effect of the Earth’s Shape on g:
The Earth is not a perfect sphere; it is slightly flattened at the poles and bulges at the equator. This means the equatorial radius of the Earth is about 21 km greater than the polar radius.
Since the acceleration due to gravity is inversely proportional to the square of the radius g ∝ 1/R² , the larger radius at the equator results in a lower value of g , while the smaller radius at the poles leads to a higher value of g.
Thus, gravity is minimum at the equator and maximum at the poles. This explains why the weight of an object increases when it is moved from the equator to the poles. The variation in g between the poles and the equator is approximately 0.5%.
Relation Between Height and Depth for the Same Change in g: The acceleration due to gravity decreases both when moving above the Earth's surface (height) and below it (depth). At a height h above the surface, gravity decreases slightly based on the distance from the Earth's center. Similarly, at a dRead more
Relation Between Height and Depth for the Same Change in g:
The acceleration due to gravity decreases both when moving above the Earth’s surface (height) and below it (depth). At a height h above the surface, gravity decreases slightly based on the distance from the Earth’s center. Similarly, at a depth d below the surface, gravity decreases because only the mass within the radius (R – d) contributes to gravity.
For the same decrease in gravity at height (h) and depth d, the relation between them can be found by comparing the two effects. It turns out that the change in gravity at a height h above the surface is the same as that at a depth d below the surface if the depth is twice the height. In other words, d = 2h.
This relationship holds true only when the height h is much smaller than the Earth’s radius, as approximations are used in this derivation. Thus, for small heights and depths, gravity behaves symmetrically with this relation.
The value of g (acceleration due to gravity) varies from place to place and depends on several factors, including: 1. Altitude – Higher altitudes result in a decrease in g . 2. Depth – The value of g changes as we go deeper into the Earth. 3. Shape of the Earth – Due to the Earth's oblate shape, g iRead more
The value of g (acceleration due to gravity) varies from place to place and depends on several factors, including:
1. Altitude – Higher altitudes result in a decrease in g .
2. Depth – The value of g changes as we go deeper into the Earth.
3. Shape of the Earth – Due to the Earth’s oblate shape, g is slightly higher at the poles and lower at the equator.
4. Rotation of the Earth – The Earth’s rotation reduces g slightly, especially near the equator.
Effect of Altitude on g: Consider the Earth as a sphere with mass M, radius R , and center O . The acceleration due to gravity at a point on the surface of the Earth depends on its mass and radius. At a height h above the Earth's surface, the gravity decreases due to the increased distance from theRead more
Effect of Altitude on g:
Consider the Earth as a sphere with mass M, radius R , and center O . The acceleration due to gravity at a point on the surface of the Earth depends on its mass and radius. At a height h above the Earth’s surface, the gravity decreases due to the increased distance from the Earth’s center.
The gravity at the Earth’s surface is proportional to (1/R²), while at a height h, it is proportional to (1/(R + h)²). By comparing the two, the ratio of gravity at the height h to gravity at the surface can be expressed as ( (R/(R + h))²).
Using the binomial theorem for approximation when h is much smaller than R, the expression simplifies to show that the change in gravity is proportional to (1 – 2h/R). This means that as h increases, gravity decreases.
For very small heights compared to the Earth’s radius, higher-order terms in h/R can be ignored. This gives an approximate linear relationship showing a decrease in gravity with height.
Key Points:
– Gravity decreases with altitude because the distance from the Earth’s center increases.
– At greater heights, such as on mountains, the value of g is less than at lower elevations or plains.
– For significant heights relative to the Earth’s radius, the more accurate proportional relationship ((R/(R + h))²) should be used. For small heights, the approximate relationship (1 – 2h/R) suffices for practical calculations.
The correct option is: (c) Both A and R are true and R explains A. Explanation: Assertion (A) states that power sharing can prevent conflict, which is supported by Reason (R) explaining how power sharing ensures the inclusion of various social groups in decision-making, ultimately reducing marginaliRead more
The correct option is:
(c) Both A and R are true and R explains A.
Explanation: Assertion (A) states that power sharing can prevent conflict, which is supported by Reason (R) explaining how power sharing ensures the inclusion of various social groups in decision-making, ultimately reducing marginalization and promoting inclusivity.
Discuss the variation of g on earth’s surface due to shape of the earth. Why does the weight of a body increase when it is taken from the equator to the pole?
Effect of the Earth's Shape on g: The Earth is not a perfect sphere; it is slightly flattened at the poles and bulges at the equator. This means the equatorial radius of the Earth is about 21 km greater than the polar radius. Since the acceleration due to gravity is inversely proportional to the squRead more
Effect of the Earth’s Shape on g:
The Earth is not a perfect sphere; it is slightly flattened at the poles and bulges at the equator. This means the equatorial radius of the Earth is about 21 km greater than the polar radius.
Since the acceleration due to gravity is inversely proportional to the square of the radius g ∝ 1/R² , the larger radius at the equator results in a lower value of g , while the smaller radius at the poles leads to a higher value of g.
Thus, gravity is minimum at the equator and maximum at the poles. This explains why the weight of an object increases when it is moved from the equator to the poles. The variation in g between the poles and the equator is approximately 0.5%.
See lessWhat is the relation between height h and depth d for the same change in g?
Relation Between Height and Depth for the Same Change in g: The acceleration due to gravity decreases both when moving above the Earth's surface (height) and below it (depth). At a height h above the surface, gravity decreases slightly based on the distance from the Earth's center. Similarly, at a dRead more
Relation Between Height and Depth for the Same Change in g:
The acceleration due to gravity decreases both when moving above the Earth’s surface (height) and below it (depth). At a height h above the surface, gravity decreases slightly based on the distance from the Earth’s center. Similarly, at a depth d below the surface, gravity decreases because only the mass within the radius (R – d) contributes to gravity.
For the same decrease in gravity at height (h) and depth d, the relation between them can be found by comparing the two effects. It turns out that the change in gravity at a height h above the surface is the same as that at a depth d below the surface if the depth is twice the height. In other words, d = 2h.
This relationship holds true only when the height h is much smaller than the Earth’s radius, as approximations are used in this derivation. Thus, for small heights and depths, gravity behaves symmetrically with this relation.
See lessWhat are the various factors on which the value of g at place on the earth depends.
The value of g (acceleration due to gravity) varies from place to place and depends on several factors, including: 1. Altitude – Higher altitudes result in a decrease in g . 2. Depth – The value of g changes as we go deeper into the Earth. 3. Shape of the Earth – Due to the Earth's oblate shape, g iRead more
The value of g (acceleration due to gravity) varies from place to place and depends on several factors, including:
See less1. Altitude – Higher altitudes result in a decrease in g .
2. Depth – The value of g changes as we go deeper into the Earth.
3. Shape of the Earth – Due to the Earth’s oblate shape, g is slightly higher at the poles and lower at the equator.
4. Rotation of the Earth – The Earth’s rotation reduces g slightly, especially near the equator.
Discuss the variation of g with altitude.
Effect of Altitude on g: Consider the Earth as a sphere with mass M, radius R , and center O . The acceleration due to gravity at a point on the surface of the Earth depends on its mass and radius. At a height h above the Earth's surface, the gravity decreases due to the increased distance from theRead more
Effect of Altitude on g:
Consider the Earth as a sphere with mass M, radius R , and center O . The acceleration due to gravity at a point on the surface of the Earth depends on its mass and radius. At a height h above the Earth’s surface, the gravity decreases due to the increased distance from the Earth’s center.
The gravity at the Earth’s surface is proportional to (1/R²), while at a height h, it is proportional to (1/(R + h)²). By comparing the two, the ratio of gravity at the height h to gravity at the surface can be expressed as ( (R/(R + h))²).
Using the binomial theorem for approximation when h is much smaller than R, the expression simplifies to show that the change in gravity is proportional to (1 – 2h/R). This means that as h increases, gravity decreases.
For very small heights compared to the Earth’s radius, higher-order terms in h/R can be ignored. This gives an approximate linear relationship showing a decrease in gravity with height.
Key Points:
See less– Gravity decreases with altitude because the distance from the Earth’s center increases.
– At greater heights, such as on mountains, the value of g is less than at lower elevations or plains.
– For significant heights relative to the Earth’s radius, the more accurate proportional relationship ((R/(R + h))²) should be used. For small heights, the approximate relationship (1 – 2h/R) suffices for practical calculations.
There are two statements given below, marked as Assertion (A) and Reason (R). Read the statements and choose the correct option. Assertion (A): Power sharing can help to prevent conflict in society. Reasoning (R): Power sharing ensures that different social groups are included in decision-making processes, reducing marginalisation and fostering inclusivity.
The correct option is: (c) Both A and R are true and R explains A. Explanation: Assertion (A) states that power sharing can prevent conflict, which is supported by Reason (R) explaining how power sharing ensures the inclusion of various social groups in decision-making, ultimately reducing marginaliRead more
The correct option is:
(c) Both A and R are true and R explains A.
Explanation: Assertion (A) states that power sharing can prevent conflict, which is supported by Reason (R) explaining how power sharing ensures the inclusion of various social groups in decision-making, ultimately reducing marginalization and promoting inclusivity.
See less