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Suppose a Planet Exists Whose Mass and Radius Both Are Half Those of the Earth. Calculate the Acceleration Due to Gravity on the Surface of this Planet. - CBSE Class 9 - Science

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Question

Suppose a planet exists whose mass and radius both are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet.

Solution

Mass and radius both are half of those of the earth
g (acceleration due to gravity) = ?
G (gravitational constant) = 6.673 × 10−11 Nm2 kg−2
M (mass of new planet)= (5.98 × 1024  kg)/2
R (radius of the earth) = (6.4 × 106 m)/2
`g = (GM)/R^2`
= `(6.673 xx 10^-11 xx 5.98 xx 10^24 xx 4)/((6.4 xx 10^6)^2 xx 2)`
= `(6.673 xx 10^-11 xx 5.98 xx 10^24 xx 4)/(6.4 xx 6.4 xx 10^12 xx 2)`              `(10^(24-11)=10^13)`
= `(6.673 xx 5.98 xx 4 xx 10^14)/(6.4 xx 6.4 xx 10^12 xx 2)`  `(10^(13-12)=10)`
= `(6.673 xx 5.98 xx 4 xx 10)/(6.4 xx 6.4 xx 2)`
= `(159.61816 xx 10)/(6.4 xx 6.4 xx 2)`
= `1.9484 xx 10` = 19.5 N

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APPEARS IN

 Lakhmir Singh Solution for Science for Class 9 Part 1 Physics (2016 to Current)
Chapter 3: Gravitation
Hots Questions | Q: 73 | Page no. 103

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Solution Suppose a Planet Exists Whose Mass and Radius Both Are Half Those of the Earth. Calculate the Acceleration Due to Gravity on the Surface of this Planet. Concept: Mass and Weight.
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