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Chapter 6: Problem 818

Direction (Read the following questions and choose) (A) If both Assertion and Reason are true and the Reason is correct explanation of assertion (B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion (C) If Assertion is true, but the Reason is false (D) If Assertion is false, but the Reason is true Assertion: The value of acc. due to gravity \((\mathrm{g})\) does not depend upon mass of the body Reason: This follows from \(\mathrm{g}=\left[(\mathrm{GM}) / \mathrm{R}^{2}\right]\), where \(\mathrm{M}\) is mass of planet (earth) and \(\mathrm{R}\) is radius of planet (earth) (a) \(\mathrm{A}\) (b) \(\mathrm{B}\) (c) \(\mathrm{C}\) (d) D

Short Answer

Expert verified
(a) A

Step by step solution

01

Review the formula for acceleration due to gravity

The formula for acceleration due to gravity is given by: \[g = \frac{GM}{R^2}\] Here, G is the gravitational constant, M is the mass of the planet (in this case, Earth), and R is the radius of the planet (Earth's radius).
02

Recognize which variables are relevant for the Assertion

The Assertion claims that acceleration due to gravity (g) doesn't depend on the mass of the body experiencing the gravitational force. In the formula for acceleration due to gravity, the mass of the body is not a variable. The mass of the planet and the radius of the planet are the only variables used.
03

Assess the Reason with respect to the Assertion

Given the formula for acceleration due to gravity, we can conclude that the mass of the body experiencing the gravitational force doesn't directly affect the value of g. In this sense, the Reason correctly explains the Assertion.
04

Choose the correct option

Based on our analysis, both the Assertion and Reason are true, and the Reason is a correct explanation of the Assertion. Therefore, the correct answer is: (a) A

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Most popular questions from this chapter

Two satellites of mass \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\left(\mathrm{~m}_{1}=\mathrm{m}_{2}\right)\) are revolving round the earth in circular orbits of \(\mathrm{r}_{1}\) and \(\mathrm{r}_{2}\left(\mathrm{r}_{1}>\mathrm{r}_{2}\right)\) respectively. Which of the following statement is true regarding their speeds \(\mathrm{V}_{1}\) and \(\mathrm{V}_{2}\) (A) \(\mathrm{V}_{1}=\mathrm{V}_{2}\) (B) \(\mathrm{V}_{1}<\mathrm{V}_{2}\) (C) \(\mathrm{V}_{1}>\mathrm{V}_{2}\) (D) $\left(\mathrm{V}_{1} / \mathrm{r}_{1}\right)=\left(\mathrm{V}_{2} / \mathrm{r}_{2}\right)$

A geostationary satellite is orbiting the earth at a height of \(5 \mathrm{R}\) above that of surface of the earth. \(\mathrm{R}\) being the radius of the earth. The time period of another satellite in hours at a height of $2 \mathrm{R}\( from the surface of earth is \)\ldots \ldots \ldots .$ hr (A) 5 (B) 10 (C) \(6 \sqrt{2}\) (D) \(6 / \sqrt{2}\)

A satellite revolves around the earth in an elliptical orbit. Its speed (A) is the same at all points in the orbit (B) is greatest when it is closest to the earth (C) is greatest when it is farthest to the earth (D) goes on increasing or decreasing continuously depending upon the mass of the satellite

If mass of a body is \(\mathrm{M}\) on the earth surface, than the mass of the same body on the moon surface is (A) \(\mathrm{M} / 6\) (B) 56 (C) \(\mathrm{M}\) (D) None of these

What is the intensity of gravitational field at the center of spherical shell (A) \(\left(\mathrm{Gm} / \mathrm{r}^{2}\right)\) (B) \(\mathrm{g}\) (C) zero (D) None of these
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