29. The acceleration due to gravity g on earth is 9.8ms?. What would t

1.	29. The acceleration due to gravity g on earth is 9.8ms?. What would the value of g for a planetwhose size is the same as that of earth but thedensity in twice that of earth?(a) 19.6 ms 2(c) 4.9 ms(b) 9.8 ms(d) 2.45 ms2
Answer» 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

29. The acceleration due to gravity g on earth is 9.8ms?. What would the value of g for a planetwhose size is the same as that of earth but thedensity in twice that of earth?(a) 19.6 ms 2(c) 4.9 ms(b) 9.8 ms(d) 2.45 ms2

Answer»

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

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