Question

The weight of a body is 630N on the surface of the earth. what will be its weight at a height R/2 above earths surface if R is the radius of the earth?​

Answer 1

Answer:

Given:

Weight of body on Earth surface is 630 N

Radius of Earth = R

To find:

Weight at a height R/2 above earth surface.

Calculation:

∴ Weight = Mass × gravity

=> 630 = M × g

=> M = 630/g .........(1)

Now , gravity at the given height is calculated as follows ;

$\boxed{ \sf{ \red{g2 = \dfrac{g}{ ({1 + \dfrac{h}{R}) }^{2} }}}}$

$\sf{ \implies g2 = \dfrac{g}{ \{{1 + \dfrac{ (\frac{R}{2} )}{R} \} }^{2} }}$

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

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

$\sf{\implies g2 = \dfrac{g}{( \dfrac{9}{4} )}}$

$\sf{\implies g2 = \dfrac{4g}{9}}$

Therefore , weight at the height :

= mass × g2

= 630/g × 4g/9

= 280 N

So final answer :

$\boxed{ \bold{ \sf{ \blue{ \huge{ 280 N}}}}}$

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

Weight of body on Earth surface is 630 N

Radius of Earth = R

To find:

Weight at a height R/2 above earth surface.

Calculation:

∴ Weight = Mass × gravity

=> 630 = M × g

=> M = 630/g .........(1)

Now , gravity at the given height is calculated as follows ;

\boxed{ \sf{ \red{g2 = \dfrac{g}{ ({1 + \dfrac{h}{R}) }^{2} }}}}

\sf{ \implies g2 = \dfrac{g}{ \{{1 + \dfrac{ (\frac{R}{2} )}{R} \} }^{2} }}

\sf{\implies g2 = \dfrac{g}{ (1 + { \dfrac{1}{2}) }^{2} }}

\sf{\implies g2 = \dfrac{g}{ ( { \dfrac{3}{2}) }^{2} }}

\sf{\implies g2 = \dfrac{g}{( \dfrac{9}{4} )}}

\sf{\implies g2 = \dfrac{4g}{9}}

Therefore , weight at the height :

= mass × g2

= 630/g × 4g/9

= 280 N

So final answer :

\boxed{ \bold{ \sf{ \blue{ \huge{ 280 N}}}}}