The value of $g$ on the earths surface is $980 c m / {s e c}^{2}$ . Its value at a height of $64 K m$ from the earth's surface is

960.40 c m / s e c^{2}

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984.90 c m / s e c^{2}

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982.45 c m / s e c^{2}

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977.55 c m / s e c^{2}

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Solution

The correct option is A $960.40 c m / s e c^{2}$
At earth's surface. $g = \frac{G M}{R^{2}} = 9.8 m / s^{2}$

$\frac{G M}{(6400 \times 10^{3})^{2}} = 9.8 m / s^{2}$ ...(1)

At a height 64 kms from earth's surface,

$\frac{G M}{((6400 + 64) \times 10^{3})^{2}} = g^{'}$ ...(2)

(1) $\div$ (2)

$(\frac{6464}{6400})^{2} = \frac{9.8}{g^{'}}$

$g^{'} = (\frac{6464}{6400})^{2} \times 9.8 = 9.6069 m / s^{2}$

$= 960.69 c m / s^{2}$

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The value of g on the earths surface is 980 cm/sec2. Its value at a height of 64 Km from the earth's surface is

The correct option is A 960.40 cm/sec2At earth's surface. g=GMR2=9.8m/s2GM(6400×103)2=9.8m/s2 ...(1)At a height 64 kms from earth's surface, GM((6400+64)×103)2=g′ ...(2)(1) ÷ (2)(64646400)2=9.8g′g′=(64646400)2×9.8=9.6069m/s2=960.69cm/s2

The value of $g$ on the earths surface is $980 c m / {s e c}^{2}$ . Its value at a height of $64 K m$ from the earth's surface is