At what distance from the centre of the earth does the gravitational acceleration have one half the value that it has on the earth's surface ?

Physics class 11th problem solution  First year physics problem solution  Gravitation problems solution

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00:00Question says, at what distance from the center of the Earth does the gravitational acceleration

00:14have half the value that it has on the Earth's surface?

00:23First of all, we will make a data, is g dash is equal to g upon 2.

00:40And we have to find radius r dash which is equal to what?

01:04Our solution is, on the surface of Earth, the value of g is calculated by the formula,

01:24g is equal to g m e upon r e square, so this is equation number 1, at certain height,

01:43the value of g is calculated by using formula, g dash is equal to g m e upon r dash square,

01:55so this is equation number 2, is g dash is obtained as g upon 2, so by placing the value of g dash

02:12in equation number 2, so g upon 2 will be equal to g m e upon r dash square,

02:22so we have to find r dash, so when we will take r dash square on the other side of equal,

02:31then this will become as r dash square upon 2 is equal to g m upon g, so here g will divide,

02:44and r dash square on the other side of equal, so r dash square will be equal to 2 into g m e upon g,

03:04so r dash square will be equal to g, because here g m e upon g, because here 2 are dividing on the other side of equal,

03:10it will multiply with g m e upon g, is r e square is equal to g m e upon g,

03:16so r dash square will be equal to g m e upon g, so r dash square will be equal to 2 into

03:33re square then we will remove this square so it will be square root on the other side of

03:45equal so r dash will be equal to under root 2 into re square so r dash will be equal to

03:55under root 2 is the under root of re square is re is the under root of 2 is 1.41 into re so this is

04:12our required answer