Question

9. Mount Everest is 8848 m above the sea level. Find the acceleration due to gravity at this height. The value of acceleration due to gravity at the earth's surface is 9.8 m/s2 and the radius of the earth is 6400km.
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Answer 1

Given :-

• Height of the Mount Everest (H) = 8848
• Acceleration due to gravity (g) = 9.8 m/s²
• Radius of the Earth (R) = 6400km
• Radius of the Earth (R) = 6400000m

To Find :-

• The acceleration due to gravity at this H = ?

Solution :-

• To calculate height the acceleration due to gravity at first we have to apply formula the acceleration due to gravity.

Formula Used :-

⇢ g' = g(1 - 2h/R)

• g' = acceleration due to gravity at the height of Mount Everest .
• g = acceleration due to gravity g = 9.8 m/s²
• h = Height of Mount Everest (h) = 8848m
• R = The radius of the Earth (R) = 6400000m

⇢g' = 9.8 × (1 - (2 × 8848)/6400000)

⇢g' = 9.8 × (1 - (2 × 1106)/800000)

⇢g' = 9.8 × (1 - 1106/400000)

⇢g' = 9.8 × {(400000 - 1106)/400000}

⇢g' = 9.8 × 398894/400000

⇢g' = 9.8 × 0.997235

⇢g' = 9.772903 m/s²

Hence,

• The acceleration due to gravity at the height of the Mount Everest (g') = 9.772903 m/s²

Answer 2

Answer:

$\large{\bf{\green{\mathfrak{\dag{\underline{\underline{Question :-}}}}}}}$

1. Mount Everest is 8848m above the sea level .Find the acceleration due to gravity at this height .The value of acceleration due to gravity at the earth surface is 9.8 m/s and radius of earth is 6400km.

$\large{\bf{\red{\mathfrak{\dag{\underline{\underline{Answer: -}}}}}}}$

• The acceleration due to gravity at the height of Mount Everest is g'=9.773m/s^2.

$\large{\bf{\purple{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• Here we know the formula of acceleration due to gravity that is ,

$g' \: = g(1 - \frac{2h}{h} )$

• If we want start our calculations we should convert km into m so ,

• The radius of earth =6400×1000=6400000m.

$\large{\bf{\green{\mathfrak{\dag{\underline{\underline{Lets begin}}}}}}}$

• Now applying all the values we get that,

• $g' = 9.8(1 - \frac{2 \times 8840}{6400000} ) = 9.8(1 - \frac{2 \times 1106}{800000} )$

• $g '= 9.8(1 - \frac{2 \times 1106}{800000} ) = 9.8(1 - \frac{1106}{400000} )$

• $g' = 9.8(400000 - \frac{1106}{400000} )$

• By doing all the calculations we get that,

• g'=9.8×0.99723=9.772m/s^2.

• g'=9.772 which is nearer to 9.773 m/s^2.

$\large{\bf{\red{\mathfrak{\dag{\underline{\underline{Therefore,}}}}}}}$

• Required answer =g'=9.772 or 9.773 m/s^2.

$\large{\bf{\purple{\mathfrak{\dag{\underline{\underline{Which is the required answer}}}}}}}$

Hope it helps u mate .

Thank you .