Question

The acceleration due to gravity on the surface of a planet whose mass is same as that of the earth and radius is half of that of the earth is: (mass of earth=6×10²⁴kg, radius of earth=6.4×10³km)
A) 35.08m/s²
B) 39.08m/s²
C) 28.08m/s²
D) 9.08m/s²
E) None of these​

Answer 1

Given data :

• mass of the planet = mass of the earth
• radius of the planet = ½ radius of the planet
• acceleration of the planet = ?

Solution : a/c to question;

• mass of the earth = 6 * 10²⁴ kg
• radius of the earth = 6.4 * 10³ km

Now, by formula of acceleration due to gravity,

• g = GM/R² ----{1}

Where,

• g is acceleration due to gravity of planet. {earth}
• G is gravitational constant {6.673 * 10^( - 11 ) Nm²/kg²}
• M is mass of the earth
• R is radius of the earth

Now, a/c to given data;

eq. {1} becomes;

⟹ g = GM/{½ R}²

⟹ g = {6.673 * 10^( - 11 ) * 6 * 10²⁴}/{½ * 6.4 * 10³}²

⟹ g = 40.038 * 10¹³/{3.2 * 10³}²

⟹ g = 40.038 * 10¹³/10.24 * 10⁶

⟹ g = 3.9099 * 10⁷ m/s²

⟹ g = 39.099 * 10⁶ m/s²

Answer : Hence, the acceleration due to gravity on the surface of a planet is 39.099 * 10⁶ m/s².

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