Question

A body weight 30N at the surface of the earth. It's weight at a height equal to half the radius of the earth will be

Answer 1

Answer:

13.33 N

Explanation:

F=GMm/r^2

30=GMm/r^2.

F at a height h is,

F=GMm/(r+h)^2

At h=r/2,

F=GMm/(3r/2)^2=4×30/9=13.33

Answer 2

The weight at height is 13.33 N.

Explanation:

Given that,

Weight = 30 N

Height $h= \dfrac{R}{2}$

We need to calculate the weight at a height

Using formula of force

For at earth surface,

$F=\dfrac{GMm}{r^2}$

$30=\dfrac{GMm}{r^2}$....(I)

For at height,

$F=\dfrac{GMm}{(r+h)^2}$....(II)

From equation (I) and (II)

$\dfrac{30}{F}=\dfrac{(r)^2}{(r+h)^2}$

$\dfrac{30}{F}=\dfrac{r^2}{(\dfrac{3r}{2})^2}$

$F=30\times\dfrac{4}{9}$

$F=13.33\ N$

Hence, The weight at height is 13.33 N.

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Topic : weight

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