The acceleration due to gravity g on earth in 9.8 ms-2. what would be the value of g for a planet whose size is the same as that of earth but the density in twice that of earth?
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∵ size of planet is same as that of earth, it means volume of planet is same as volume of earth.
So, the radius of planet = radius of earth = R {let }
Also we know, density = mass/volume ,
If volume is constant then density depends upon mass and it is directly proportional to mass.
A/C to question,
density of planet is twice that of earth.
∴mass of planet is twice that of earth.
Let mass of earth is M
Then mass of planet is 2M
Now, g = GM/R² , for earth
g' = G(2M)/R² , for planet .
Here you observed , 2g = g'
Hence, acceleration due to gravity on surface of planet is two times of acceleration due to gravity on Earth's surface.
E.g., acceleration due to gravity on planet' surface = 2 × 9.8 = 19.6 m/s²
So, the radius of planet = radius of earth = R {let }
Also we know, density = mass/volume ,
If volume is constant then density depends upon mass and it is directly proportional to mass.
A/C to question,
density of planet is twice that of earth.
∴mass of planet is twice that of earth.
Let mass of earth is M
Then mass of planet is 2M
Now, g = GM/R² , for earth
g' = G(2M)/R² , for planet .
Here you observed , 2g = g'
Hence, acceleration due to gravity on surface of planet is two times of acceleration due to gravity on Earth's surface.
E.g., acceleration due to gravity on planet' surface = 2 × 9.8 = 19.6 m/s²
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