Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Gravitation PYQ — JEE Main 2022 · 27 Jun · Shift 1 · Q48 with Solution

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Correct answer: A

Analyze Statement I

Statement I says: The law of gravitation holds good for any pair of bodies in the universe.

Newton’s law of gravitation states that any two masses attract each other with force $F = G\frac{m_1 m_2}{r^2}$ where $m_1$ and $m_2$ are the masses and $r$ is the distance between them.

This law is universal in nature, so it applies to any pair of bodies having mass.

Hence, Statement I is true.
Analyze Statement II

Statement II says: The weight of any person becomes zero when the person is at the centre of the earth.

Weight is given by $W = mg$ where $g$ is the gravitational acceleration.

At the centre of the earth, due to symmetry, gravitational pulls from all sides cancel each other. Therefore, $g = 0$ and so, $W = m \times 0 = 0$

Hence, Statement II is true.
Choose the correct option

Since both Statement I and Statement II are true, the correct option is:

$\boxed{A}$
Comparison with stored answer

Stored correct answer: A

My derived answer: A

Therefore, they agree.