What would be the value of g on the sur...

What would be the value of g on the surface of the earth if its mass was twice and its radius half of what it is now ?

Text Solution

Verified by Experts

`g=(GM)/(R^(2))`
`therefore g_(1)=(GM_(1))/(R_(1)^(2))" and "g_(2)=(GM_(2))/(R_(2)^(2))`
`therefore" "(g_(2))/(g_(2))=((M_(2))/(M_(1)))((R_(1))/(R_(2)))^(2)=2(2)^(2)=8`
`" "(because M_(2)=2M_(1) and R_(2)=(R_(1))/(2))`
`therefore g_(2)=8g_(1)`
Thus, the, value of g on the surface of the earth woule be eight times the present value.

Topper's Solved these Questions

GRAVITATION
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise QUESTIONS & ANSWERS|45 Videos
GRAVITATION
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Answer the following questions :|53 Videos
GRAVITATION
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Think about it|4 Videos
GIVE SCIENTIFIC REASONS
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise CHAPTER 10 : DISASTER MANAGEMENT|2 Videos
HEAT
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise NUMERICAL PROBLEMS FOR PRACTICE|12 Videos

What would be the acceleration due to gravity on the surface of a planet if its radius is (1)/(4) the radius of the earth and its mass is (1)/(80) th the mass of the earth ?

`g_(p)=(g)/(2)`

`g_(p)=(g)/(5)`

`g_(p)=(g)/(3)`

`g_(p)=(g)/(4)`

The height at which the value of g is half that on the surface of the earth of radius R is

`R`

`2R`

`0.414 R`

`0.75R`

If g is the acceleration due to gravity on the surface of the earth , its value at a height equal to double the radius of the earth is

`g/2`

`g/3`

`g/9`