Question

24. Weight of an object is 294 N on the surface of the earth. What is its weight at a height of 200 km from the surface of the earth. Radius of the earth= 6400 km.

Answer 1

soln:

Let  GMm = k

we know,

F = GMm/r²

F = k/r²

294 N = k/(6400 km)²

k = 294 N × (6400 km)²-------------------------------1

now  when the distance is 200 km above the surface of the earth

R = 6600 km

F = GMm/R²

F = 294 N × (6400 km)²/(6600 km)²

F = 276.5 N (approx)

therefore weight of the body at a height of 200 km from the surface of the earth = 276.5 N (approx)

Answer 2

$\huge‏‏ \bold \red{Answer}$

$\bf \: W_h \: = mg_h$

$\bf = \: mg( \frac{R}{R + h} ) ^{2}$

$\bf \: [g_h \: = \: g (\: \frac{R}{R + h \: } )^{2} ]$

Here mg = 294N, R = 6400 km, h = 200km

$\bf \: \therefore \: ‎‎ ‎‎ ‎ ‎‎ ‎ ‎ ‎‎ ‎ ‎W_h \: = \: 294 \: [ \frac{6400}{6400 \: + \: 200} ]^{2}$

$\bf \: ‎ ‎ ‎ ‎‎ ‎ ‎ ‎‎ = \: ‎294 \: [ \: \frac{6400}{6600} ]^{2}$

$\bf \: ‎ ‎ ‎ ‎‎ ‎ ‎‎ ‎‎ ‎ ‎ ‎= \: 276.45 \: N$

★ Note:-

Weight decreases with increase of height from the surface of the earth.