Question

If an object at a distance 6.4*10^6m from the centre of the earth weight 10N,what will be its weight when it is shiftad to the distance of 1.2*10^7m from the centre of the earth?

Answer 1

We know that radius of Earth is 6.4 × 10^6 m.

The weight of an object at the surface of earth is said to be 10 N.

To find:

Weight at height of 1.2 × 10^7 m

Calculation:

Let's find the gravitational acceleration at that height :

$g2 = \dfrac{g}{ {(1 + \dfrac{h}{r} )}^{2} }$

$= > g2 = \dfrac{g}{ {(1 + \dfrac{120 \times {10}^{5} }{64 \times {10}^{5} } )}^{2} }$

$= > g2 = \dfrac{g}{ {(1 + 2 )}^{2} }$

$= > g2 = \dfrac{g}{ {(3)}^{2} }$

$= > g2 = \dfrac{g}{9}$

So the gravitational acceleration has decreased by 9 times :

So new weight will be :

New Wt = mg/9 = 10/9 = 1.11 N.