Question

Assertion: The value of acceleration due to gravity does not depend on the mass of the body.

Reason: Acceleration due to gravity is a constant quantity.

• A. Both Assertion and Reason are true. Reason is the correct explanation of Assertion.
• B. Both Assertion and Reason are true. Reason is not the correct explanation of Assertion.
• C. Assertion is true and Reason is false.
• D. Both Assertion and Reason are false.

Answer 1

The correct option is C

Assertion is true and Reason is false.

1. Acceleration due to gravity: The acceleration achieved by any object due to the gravitational force of attraction by the earth is called acceleration due to gravity by the earth.
2. As each planet has a different mass and radius so the acceleration due to gravity will be different for a different planet.
3. Acceleration due to gravity of the earth having mass $\left(M\right)$ and radius $\left(R\right)$ on earth surface is given by: $g=\frac{GM}{R^2}$ here $\mathrm{G}$ is the universal gravitational constant.
4. Acceleration due to gravity at any depth (h) of the earth's surface whose distance from the center of the earth is $r$ is given by: $g\text{'}=\frac{gr}{R}$.
5. Acceleration due to gravity at height $h\text{'}$ whose distance from the center of the earth is $r$ is given by: $g\text{'}=\frac{g{R}^2}{r{\text{'}}^2}$. Here, $\mathrm{G}$ is Universal gravitational constant, $r=(R-h)$ and $r\text{'}=(R+h).$
6. Here $M$ is the mass of the earth, not of any other body. So the acceleration due to gravity is independent of the mass of the body which means Assertion is true.
7. Also the acceleration due to gravity changes with respect to the height above the earth or depth below the earth's surface.
8. Thus, acceleration due to gravity is not a constant quantity as for some range of the height above the earth or for long height/depth, it changes. So, Reason is false.

Hence, option (C) is correct.