2) At what distance from Earth's surface is the acceleration due to gravity 7.33m/s^2 (9.97times 10^5m)

Here's how to solve this problem:<br /><br />**1. Understand the concept:**<br /><br />The acceleration due to gravity (g) decreases as you move further away from the Earth's center. The relationship is given by Newton's Law of Universal Gravitation:<br /><br />g = (G * M) / r²<br /><br />Where:<br /><br />* g is the acceleration due to gravity<br />* G is the gravitational constant (6.674 x 10⁻¹¹ N⋅m²/kg²)<br />* M is the mass of the Earth (5.972 x 10²⁴ kg)<br />* r is the distance from the center of the Earth<br /><br />**2. Set up the equation:**<br /><br />We are given g = 7.33 m/s² and we want to find r. We know G and M.<br /><br />7.33 m/s² = (6.674 x 10⁻¹¹ N⋅m²/kg² * 5.972 x 10²⁴ kg) / r²<br /><br />**3. Solve for r:**<br /><br />* Multiply both sides by r²:<br /><br />7.33 m/s² * r² = (6.674 x 10⁻¹¹ N⋅m²/kg² * 5.972 x 10²⁴ kg)<br /><br />* Divide both sides by 7.33 m/s²:<br /><br />r² = (6.674 x 10⁻¹¹ N⋅m²/kg² * 5.972 x 10²⁴ kg) / 7.33 m/s²<br /><br />r² ≈ 5.456 x 10¹³ m²<br /><br />* Take the square root of both sides:<br /><br />r ≈ 7.386 x 10⁶ m<br /><br />**4. Calculate the distance from Earth's surface:**<br /><br />The value of 'r' we calculated is the distance from the *center* of the Earth. To find the distance from the *surface*, we need to subtract the Earth's radius (R), which is approximately 6.371 x 10⁶ m.<br /><br />Distance from surface = r - R<br /><br />Distance from surface ≈ 7.386 x 10⁶ m - 6.371 x 10⁶ m<br /><br />Distance from surface ≈ 1.015 x 10⁶ m or 1015 km<br /><br />**Therefore, the distance from the Earth's surface where the acceleration due to gravity is 7.33 m/s² is approximately 1.015 x 10⁶ m or 1015 km.** The provided answer of 9.97 x 10⁵ m is incorrect.<br />