00:01
Hello, we have a question in which it is related to the gravitational force that the sun exerts on the moon.
00:11
Okay, so it is given that gravitational force that sun exerts on the moon is perpendicular to the gravitational force that earth exerts on the moon.
00:20
So let us assume that gravitational force on moon due to sun is this? and the gravitational force of a gravitational force on moon due to earth is this okay so this will be vector these two will be the vector quantities now certain things are being given that distance between the sun and moon sun and moon that is r s m is r s m and distance between earth and moon that is e m okay so we we have been provided with our s m that distance between sun and moon is 1 .50 into 10 to power 11 meters and distance between earth and moon equal to 3 .85 into 10 to power 8 meter and mass of sun ms is being given as 1 .99 into 10 at the power 30 kg on mass of earth is 5 .98 into 10 to power 24 kg and mass of the moon equal to 7 .35 into 10 to power 22 kg okay okay now we have to get the things done right now what all we need to do is we have to just remember the force of gravitation that is gravitational force which is always g m1 m2 by r squared so this is the normal gravitational force according to newton's law of gravitation so if we want to calculate force on moon due to sun so let's talk only about magnitude that is force on moon due to sun it should be equal to g which is universal gravitational constant mass of moon into mass of sun divided by r distance between sun and moon that is s m s m whole square similarly if we need to calculate this force exerted by moon on earth it will be force exerted by moon on earth g mass of moon and mass of earth divided by distance between these two that is r e whole square okay now one thing to be noted here that these two are vector quantities and angle between these two is always 90 degree it is being given that these two are perpendicular so resultant force resultant force we need to calculate magnitude of the net gravitational force that is the resultant force let us write it as f g will be simply equal to will be simply equal to f force on moon exerted by sun whole square the force on moon exerted by earth whole square so let us plug in the values so f g will be equal to a g mass of moon and mass of sun by i r s m whole square plus g mass of moon into mass of earth divided by r e m whole square under the square root okay now this could be written like g square mass of moon whole square this should be taken as common or we should just move ahead we'll be taking it next step by r s m whole square plus g square mass of moon whole square mass of earth whole square divided by r e m whole square and a root now let us think what all things should be common g square and mass of moon whole square so they should be taken outside it will be gm okay mass of moon and remaining terms will be mass of sun whole square by r sm whole square plus mass of earth whole square by r e m whole square now let us start plugging values g will be equal to that is universal gravitational constant which is always equal to 6 .67 into 10 to power minus 11 neutermeter square per kg square okay under the square root mass of sun whole square okay, okay, okay, okay, one more thing i have left, that is mass of moon.
06:33
So mass of moon is being given as 7 .35 into 10 .5.
06:39
22 kg, yes, 7 .35 into 10 to power 22 kg, yes.
06:50
And into under the square root certain things, which are mass of sun whole square, that is 1 .9.
07:01
9 into 10 to the power 30 okay 10 to the power 30 kg whole square by 1 .50 into 10 raised to the power 11 meter k okay one thing i have missed it out okay yes this was already whole square this was already whole square i have missed it's whole square so it will be raised to the power four sorry sorry it should be raised to the power four yes raised to the power four plus and mass of earth is at 5 .98 into 5198 into 10 to power 24 kg divided by a kg whole square divide by 3 .85 into 10 to the power 8 meter raised to the power 4 under the square root okay so let us start solving this 6 .67 6 .67 into 7 .35 that is 49 .0245 into 10 power 11 it will be because this is 22 and 10 to power minus 11 so it will be 11 newton meter is square one kg will be cancelled out okay so so square root let us write it as 1 .99 whole square divided by 1 .50 raised to the power 4 k so this is 0 .782 to 4 and 10 to the power 30 10 to the power 44 60 40 60 44 that is 16 so it will become 0 .7822 into 10 degrees of power 16 kg squared by meter 4 plus what will this be 5 .98 whole square divided by 3 .85 raised to the power 4 okay this will be 0 .1627 0 .1627 into 10 to the power this will be 48 minus 327 kg square and less to the power 4 okay now let us use calculator for this what will be like 0 .171627 plus 0 .7822 and this will be 49 .0245 into 10 of power 11 newton meter square per kg and the root 0 .9 .9 .9.
10:53
496 into 10 to power 16 kg square by meter raised with power 4 so it's a square root 0 .94496 square root 4496 square root 4496 square root 0 .97 so this will become 49 .02445 into 10 to power 11 newton meter square per kg into 0 .9 .97209 into 10 .5 .8 kg by meter square.
11:46
So meter square, meter, kg will get cancelled out.
11:50
We will be having to 49 .0245...