Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason R : At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below:

Both A and R are true and R is the correct explanation of A.

Both A and R are true but R is NOT the correct explanation of A.

Gravitation PYQ — JEE Main 2022 · 26 Jun · Shift 2 · Q51 with Solution

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Correct answer: D

Interpret the assertion

Assertion A says that while moving from pole to equator:
- the direction of acceleration due to gravity always points towards the center of Earth, and
- there is no variation in its magnitude.
Check the magnitude part of Assertion A

The effective acceleration due to gravity on Earth varies with latitude because of:
- Earth's rotation, and
- Earth's oblate shape.
In particular,
- at the poles: centrifugal effect is zero, so $g$ is maximum,
- at the equator: centrifugal effect is maximum, so effective $g$ is minimum.
Hence, the magnitude of $g$ does vary from poles to equator.

Therefore, Assertion A is false.
Check the direction part carefully

At the equator, the centrifugal acceleration is directed outward along the radius, and gravitational attraction is toward the center. Since both are along the same radial line, the effective acceleration due to gravity remains directed towards the center of Earth.

So Reason R is true.
Evaluate the reason

Reason R states only that at equator, the direction of acceleration due to gravity is toward the center of Earth. This is correct.

But Assertion A claims a much stronger statement: that from poles to equator the direction always points toward the center without any variation in magnitude. Since the magnitude definitely changes, Assertion A is false.
Choose the correct option
- Assertion A: False
- Reason R: True
Therefore, the correct option is: $\boxed{\text{D}}$

View written solutionFree

Correct answer: D

Interpret the assertion

Assertion A says that while moving from pole to equator:
- the direction of acceleration due to gravity always points towards the center of Earth, and
- there is no variation in its magnitude.
Check the magnitude part of Assertion A

The effective acceleration due to gravity on Earth varies with latitude because of:
- Earth's rotation, and
- Earth's oblate shape.
In particular,
- at the poles: centrifugal effect is zero, so $g$ is maximum,
- at the equator: centrifugal effect is maximum, so effective $g$ is minimum.
Hence, the magnitude of $g$ does vary from poles to equator.

Therefore, Assertion A is false.
Check the direction part carefully

At the equator, the centrifugal acceleration is directed outward along the radius, and gravitational attraction is toward the center. Since both are along the same radial line, the effective acceleration due to gravity remains directed towards the center of Earth.

So Reason R is true.
Evaluate the reason

Reason R states only that at equator, the direction of acceleration due to gravity is toward the center of Earth. This is correct.

But Assertion A claims a much stronger statement: that from poles to equator the direction always points toward the center without any variation in magnitude. Since the magnitude definitely changes, Assertion A is false.
Choose the correct option
- Assertion A: False
- Reason R: True
Therefore, the correct option is: $\boxed{\text{D}}$