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The mean diameter of earth Mars and Earth are 6.9x10^3 km and 1.3x10^4 km . The mass of Mars is 0.11 times the mass of Earth 1) What is the ratio of Mean Density of Mars to that of Earth? 2) What is the value of Gravitational Acceleration and Escape Speed on Mars ?

The mean diameter of earth Mars and Earth are 6.9x10^3 km and 1.3x10^4 km . The mass of Mars is 0.11 times the mass of Earth 


1) What is the ratio of Mean Density of Mars to that of Earth? 


2) What is the value of Gravitational Acceleration and Escape Speed on Mars ?

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
9 years ago
Ans 1)
The ratio of mean densities of earthand mars can be calculated by:

Taking the mass of earth to be m
mass of mars to be 0.11 m
vloume of earth= 4/3*pi*r^3= 4/3*pi*(1.3/2 *10^7)^3 [As 1.3x10^4 is the diameter]
Same for mars =4/3*pi*r^3= 4/3*pi*(6.9/2 *10^6)^3

The density of a sphere(considering the earth and mars to be a perfect sphere)=mass/volume

Calculating the ratios, the mass of earth would cancel out leaving behind a numerical value.

Same can be done for the second part by calculating the gravitational acceleration of mars in terms of ‘g’ and then putting the value of ‘g’ to get tyhe value of ‘g’ for mars

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