{"id":1854,"date":"2018-04-15T11:54:01","date_gmt":"2018-04-15T03:54:01","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1854"},"modified":"2023-08-09T08:22:37","modified_gmt":"2023-08-09T08:22:37","slug":"gravitational-field-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/gravitational-field-problems-and-solutions.htm","title":{"rendered":"Gravitational field – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Gravitational field – problems and solutions<\/span><\/p>\n

1. What is the ratio of the gravitational field<\/a> of the object A and the object B?<\/span><\/p>\n

\"Gravitataional<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Mass<\/a> of object A (mA<\/sub>) = 1<\/span><\/p>\n

Mass of object B (mB<\/sub>) = 2<\/span><\/p>\n

Distance of the object A from planet Earth (rA<\/sub>) = 1<\/span><\/p>\n

The distance of the object B from planet Earth (rB<\/sub>) = 2<\/span><\/p>\n

Wanted:<\/u> The ratio of the gravitational field of the object A and the object B<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The equation of the gravitational field of the Earth :<\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

g = the magnitude of the gravitational field, G = gravitational constant, mB<\/sub> = mass of Earth, rB<\/sub> = radius of Earth<\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

The ratio of the gravitational field :<\/span><\/p>\n

gA<\/sub> : gB<\/sub><\/span><\/p>\n

G : G\/2<\/span><\/p>\n

1 : 1\/2<\/span><\/p>\n

2 : 1<\/span><\/p>\n

2. If the position of the object A is 0.5R above the surface of the Earth, while the position of the object B is 2R above the surface of the Earth, then what is the ratio of the gravitational field that experienced by object A and object B. R is the radius of the Earth.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The distance of the object A from the center of the Earth = 0.5R + R = 1.5R = 1.5<\/span><\/p>\n

The distance of the object B from the center of the Earth = 2R + R = 3R = 3<\/span><\/p>\n

Wanted:<\/u> The ratio of the gravitational field <\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The gravitational field experienced by object A (gA<\/sub>) :<\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

The gravitational field experienced by object B (gB<\/sub>) :<\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

The ratio of <\/u>the gravitational field <\/u>experienced by the object A and the object B :<\/u><\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

3. The gravitational field at the surface of the Earth is g, then what is the gravitational field at the height of 1.5R above the surface of the Earth. R = the radius of the Earth.<\/span><\/p>\n

Solution<\/u><\/span><\/p>\n

The force of gravity (F) is directly proportional to the gravitational field (g). The greater the force of gravity, the greater the gravitational field. <\/span><\/p>\n

The gravitational force (F) is directly proportional to 1\/r<\/span>2<\/span><\/sup>, where r = the distance of an object from the center of the earth. The force of gravity is directly proportional to 1\/r<\/span>2<\/span><\/sup> so that the gravitational field (g) is also proportional to 1\/r<\/span>2<\/span><\/sup>.<\/span><\/span><\/p>\n

When the astronaut is on the surface of the Earth that is R (R = radius of the earth) from the center of the earth, the gravitational field is g. This can be proven through the following calculations:<\/span><\/p>\n

The gravitational field (g) is proportional to 1 \/ R2<\/sup>. If R = 1 then 1 \/ R2<\/sup> = 1\/12<\/sup> = 1\/1 = 1. If the distance of the astronaut from the center of the earth = 1 then astronaut experiences the gravitational field of = (g) (1) = g.<\/span><\/p>\n

The distance of the astronaut from the center of the earth is 1.5R = 1.5 (1) = 1.5 then astronaut undergoes a gravitational field of : 1 \/ R2<\/sup> = 1 \/ 1.52<\/sup> = 1 \/ 2.25. So if the astronaut distance from the center of the earth = 1.5 then astronaut has a gravitational field of = (g) (1 \/ 2.25) = g \/ 2.25<\/span><\/p>\n

4. What is t<\/span>he ratio of the earth’s gravitational field <\/span>for <\/span>two objects, one <\/span>at <\/span>the surface of the earth and another at the <\/span>height of <\/span>\u00bd R <\/span>from <\/span>the earth’s surface (R = the radius of the earth)?<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The distance of the object A from the center of the earth (rA<\/sub>) = R = 1<\/span><\/p>\n

The d<\/span>istance of <\/span>the <\/span>object B from <\/span>the <\/span>center of <\/span>the <\/span>earth (r<\/span>B<\/span><\/sub>) = 0.5R + R = 1.5R = 1.5<\/span><\/span><\/p>\n

Wanted:<\/u> T<\/span>he ratio of the earth’s gravitational field<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

T<\/span>he earth’s gravitational field experienced by object A (g<\/span>A<\/span><\/sub>) :<\/span><\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

T<\/span>he earth’s gravitational field experienced by object A (g<\/span>B<\/span><\/sub>) :<\/span><\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

T<\/span>he ratio of the earth’s gravitational fiel<\/span>d <\/span>experienced by object A <\/span>and object B :<\/span><\/span><\/p>\n

\"Gravitational<\/span><\/p>\n

    \n
  1. What is a gravitational field?<\/strong><\/span>\n