Question

53. A recently discovered planet has a mass four times as great as Earth's and a radius twice as large as Earth's. What will be the approximate size of its gravitational field?

Answer 1

The approximate size of the gravitational field of the recently discovered planet will be the same as Earth's, which is 9.8 m/s².

Step-by-step explanation:

To determine the approximate size of the gravitational field of the recently discovered planet, we can use the formula for gravitational field strength:

g = G imes rac{M}{r^2}

where:

• g is the gravitational field strength
• G is the gravitational constant (~6.67 x 10-11 Nm2/kg2)
• M is the mass of the planet
• r is the radius of the planet

Given that the planet has a mass four times as great as Earth's (4 imes MEarth) and a radius twice as large as Earth's (2 imes rEarth), we can substitute these values into the formula:

g = 6.67 imes 10-11 imes rac{4 imes MEarth}{(2 imes rEarth)^2}

Simplifying the equation, we have:

g = rac{4}{4} imes rac{G imes MEarth}{rEarth^2}

Since the mass and radius of Earth cancel out, the gravitational field strength of the new planet will be the same as Earth's.

Therefore, the approximate size of its gravitational field is 9.8 m/s².

Answer 2

`g' = g = 9.81 m/s^2`

so gravity will be same as that of surface of earth

Step-by-step explanation:

As we know that the acceleration due to gravity is given as

`g = (GM)/(R^2)`

here we have

`M = 4M_e`

`R = 2R_e`

we know that for earth we have

`g = 9.81 = (GM_e)/(R_e^2)`

now if the radius and mass is given as above

`g' = (G(4M_e))/((2R_e)^2)`

`g' = (GM_e)/(R_e^2)`

`g' = g = 9.81 m/s^2`

so gravity will be same as that of surface of earth