Chapter : 4. Gravitation
Examples of Mass & Weight
Example : 6
Calculate the value of acceleration due to gravity on a planet whose mass is 4 times as that of the earth and radius is 3 times as that of the earth.
Solution. If M is the mass of the earth and R is the radius of earth, the value of acceleration due to gravity on the earth (ge) is given by
...(1)
Let us consider a planet such that mass of the planet is equal to 4 times the mass of earth. Mp = 4M
Radius of the planet is equal to 3 times the radius of earth.
Re = 3R
Then, acceleration due to gravity on this planet(gp) is
...(2)
Dividing equation (2) by equation (1), we get
Thus, acceleration due to gravity on the given planet is 4.35 m/s2.
Example : 7
Given the mass of the moon = 7.35 × 1022 kg and the radius of the moon = 740 km. Calculate the acceleration experienced by a particle on the surface of the moon due to the gravitational force of the moon. Find the ratio of this acceleration to that experienced by the same particle on the surface of the earth.
Solution. If Mm is the mass of the moon and Rm is its radius, then the acceleration experienced by a body on its surface is given by
a =
Here, Mm = 7.3 × 10<22 kg;
Rm = 1740 km = 1.74 × 106 m
∴
While the acceleration due to gravity on the surface of the earth, is given by
Comparing acceleration due to gravity on moon to that on the earth is
Calculate the value of acceleration due to gravity on a planet whose mass is 4 times as that of the earth and radius is 3 times as that of the earth.
Solution. If M is the mass of the earth and R is the radius of earth, the value of acceleration due to gravity on the earth (ge) is given by
...(1)Let us consider a planet such that mass of the planet is equal to 4 times the mass of earth. Mp = 4M
Radius of the planet is equal to 3 times the radius of earth.
Re = 3R
Then, acceleration due to gravity on this planet(gp) is
...(2)Dividing equation (2) by equation (1), we get
Thus, acceleration due to gravity on the given planet is 4.35 m/s2.
Example : 7
Given the mass of the moon = 7.35 × 1022 kg and the radius of the moon = 740 km. Calculate the acceleration experienced by a particle on the surface of the moon due to the gravitational force of the moon. Find the ratio of this acceleration to that experienced by the same particle on the surface of the earth.
Solution. If Mm is the mass of the moon and Rm is its radius, then the acceleration experienced by a body on its surface is given by
a =
Here, Mm = 7.3 × 10<22 kg;
Rm = 1740 km = 1.74 × 106 m
∴
While the acceleration due to gravity on the surface of the earth, is given by
Comparing acceleration due to gravity on moon to that on the earth is
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