Question

Calculate the force of gravitation due to the earth on a stone of 1kg mass lying on the ground.
Take:Mass of earth = 6.4 × 10^24 kg; Radius of earth = 6.4 ×10^3 km; and G = 6.7×10^-11 Nm^2 kg^-2.​

Answer 1

$\bf{\underline{\underline{Answer:}}}$

$\bf{F = 10.47 N}$

$\bold{\underline {Given:}}$

Gravitational constant, ${G} = 6.7 × {10}^{-11}N{m}^{2} k{g}^{-2}$

Mass of earth, ${m}_{1}=6.4×{10}^{24}kg$

Mass of stone, ${m}_{</strong><strong>2</strong><strong>}=</strong><strong>1</strong><strong>kg$

Radius of earth $</strong><strong>=</strong><strong> </strong><strong>6.4</strong><strong> </strong><strong>×</strong><strong> </strong><strong>{</strong><strong>10</strong><strong>}</strong><strong>^</strong><strong>{</strong><strong>3</strong><strong>}</strong><strong>$

$\bold{\underline {</strong><strong>To</strong><strong> </strong><strong>find</strong><strong>:}}$

$⟹ {</strong><strong>Force</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>of</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>gravitation</strong><strong>}</strong><strong> </strong><strong>=</strong><strong> </strong><strong>{</strong><strong>?</strong><strong>}$

$\bf{\underline{\underline{</strong><strong>Step</strong><strong> </strong><strong>-</strong><strong> </strong><strong>by</strong><strong> </strong><strong>-</strong><strong> </strong><strong>step</strong><strong>\</strong><strong>:</strong><strong>explanation</strong><strong>:}}}$

Distance between the center of the earth and the stone,

${</strong><strong>r</strong><strong>}$= Radius of earth

${R} _{e} = {6.4 × {10}^{3}km}$

$= {6.4 × {10}^{3}×1000m}$

$= 6.4 × {10}^{</strong><strong>6</strong><strong>} </strong><strong>m</strong><strong>$

We know that,

${F} =G ×\dfrac{{m}_{1}{m}_{2}}{{r}^{2}}$

Substituting these values in the above formula, we get

${F} =\dfrac{6.7 × {10}^{-11}×6.4×{10}^{24}×1}{{(6.4×{10}^{6})}^{2}}$

$\bf{F = 10.47 N}$

$<hr style ="border:1px solid red;"/>$$<b> <p style="color:green;">Thus, the earth exerts a gravitational force of 10.47 N on a stone of mass 1 kilogram. </p></b>$$<hr style ="border:1px solid red;"/>$

$<b><h3>#Be_Brainly </h3></b>$

Answer 2

Answer:

F=GMm /R^2 M=Mass of the earth =6 x10*24kg m=mass of the body=1kg,R= Radius of the earth=6.4 x10*3m,G=Gravitational constant=6.67 x10*-11Nm*2/kg*2 then F=6.67 x10*-11x6 x10*24 x1/6.4 x6.4 x10*3 x10*3 =6.67 x6 x10*13/6.4 x6.4 x10*6 =667 x6 x10*7/64 x64=0.97705 x10*7 =9.7705 x10*6N