Question

calculate the value acceleration due to gravity on the surface of a planet x having a mass of 5*10^20 kg and radius 1800 km.

Answer 1

0.0103 m/s² is the required answer.

GIVEN:

• Mass of the planet, M = 5 × 10²⁰ kg
• Radius of the planet, R = 1800 km

TO FIND:

Acceleration due to gravity on the surface of the planet ,g

FORMULA:

g = GM/R²

Where G is universal gravitational constant.

G = 6.67 × 10^-11 Nm²/kg

SOLUTION:

STEP 1: TO CONVERT RADIUS IN STANDARD UNIT:

• The SI unit of radius is metre, m
• 1 km = 1000 m
• 1800 km = 1800 × 1000 m
• Radius , R = 18 × 10⁵ m

STEP 2: TO FIND ACCELERATION DUE TO GRAVITY:

g = GM/R²

$g = \dfrac{6.67 \times {10}^{ - 11} \times 5 \times {10}^{20} }{ ({18 \times {10}^{5} )}^{2} } \\ \\ g = \dfrac{6.67 \times 5 \times {10}^{9} }{18 \times 18 \times {10}^{10} } \\ \\ g = \dfrac{33.35}{324 \times 10} \\ \\ g = \dfrac{33.35}{3240} \\ \\ g = 0.01029 \\ \\ g = 0.0103 \: \dfrac{m}{ {s}^{2} }$

ANSWER:

Acceleration due to gravity on the planet X is 0.0103 m/s²

ACCELERATION DUE TO GRAVITY:

• It varies on different planet.

• It depends on mass and radius of the planet.

• It is independent on the mass of the body on which it is acting.

• The variation of g also depends on lattitude, depth and rotational effect of a planet.

• Acceleration due to gravity acts towards the centre of the planet.

Answer 2

Answer:

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