SATHEE: Gravitation Question 106

Gravitation Question 106

Question: The magnitudes of the gravitational force at distances $[r_{1}]$ and $[r_{2}]$ from the centre of a uniform sphere of radius R and mass M are $[F_{1}]$ and $[F_{2}]$ respectively. Then[IIT 1994]

Options:

A) $[\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}]$ if $[r_{1} < R]$ and $[r_{2} < R]$

B) $[\frac{F_{1}}{F_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}}]$ if $[r_{1} > R]$ and $[r_{2} > R]$

C) $[\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}]$ if $[r_{1} > R]$ and $[r_{2} > R]$

D) $[\frac{F_{1}}{F_{2}} = \frac{r_{2}^{2}}{r_{1}^{2}}]$ if $[r_{1} < R]$ and $[r_{2} < R]$

Show Answer

Answer:

Correct Answer: A

Solution:

$[g = \frac{4}{3} π ρ G r]$ \ $[g \propto r]$ if $[r < R]$ $[g = \frac{G M}{r^{2}}]$ \ $[g \propto \frac{1}{r^{2}}]$ if $[r > R]$ If $[r_{1} < R]$ and $[r_{2} < R]$ then $[\frac{F_{1}}{F_{2}} = \frac{g_{1}}{g_{2}} = \frac{r_{1}}{r_{2}}]$ If $[r_{1} > R]$ and $[r_{2} > R]$ then $[\frac{F_{1}}{F_{2}} = \frac{g_{1}}{g_{2}} = {(\frac{r_{2}}{r_{1}})}^{2}]$

Gravitation Question 106

Question: The magnitudes of the gravitational force at distances $[r_{1}]$ and $[r_{2}]$ from the centre of a uniform sphere of radius R and mass M are $[F_{1}]$ and $[F_{2}]$ respectively. Then[IIT 1994]

Options:

Answer:

Solution:

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Gravitation Question 106

Question: The magnitudes of the gravitational force at distances [r1] and [r2] from the centre of a uniform sphere of radius R and mass M are [F1] and [F2] respectively. Then[IIT 1994]

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The magnitudes of the gravitational force at distances $[r_{1}]$ and $[r_{2}]$ from the centre of a uniform sphere of radius R and mass M are $[F_{1}]$ and $[F_{2}]$ respectively. Then[IIT 1994]