(2.) A sphere of mass 40 kg is attracted by a second sphere of mass 50 kg with a force 0.02 g wt. Calculate the distance between them. Use G = 6.67 x 10¹¹ N m² kg 2. [Ans. 2.6 cm] give me proper solution
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(2.) A sphere of mass 40 kg is attracted by a second sphere of mass 50 kg with a force 0.02 g wt. Calculate the distance between them. Use G = 6.67 x 10¹¹ N m² kg 2. [Ans. 2.6 cm] give me proper solution
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Answer:
F = Gm1m2r^2 =>40 x 10 = 6.67 x 10^-11 x 60 x 40r^2 =>r^2 = 0.00002m
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To calculate the distance between the two spheres, we can use the formula for gravitational force:
Force = (G * mass1 * mass2) / distance²
Given that the force is 0.02 g wt, we need to convert it to Newtons:
0.02 g wt = 0.02 kgf = 0.02 kg * 9.8 m/s² = 0.196 N
Now we can rearrange the formula to solve for distance:
distance² = (G * mass1 * mass2) / Force
distance² = (6.67 x 10¹¹ N m² kg² / (kg²)) * (40 kg * 50 kg) / 0.196 N
distance² = (6.67 x 10¹¹ N m²) * (40 kg * 50 kg) / 0.196 N
distance² = (6.67 x 10¹¹ N m²) * (2000 kg²) / 0.196 N
distance² = (6.67 x 10¹¹ N m²) * (2000 kg²) / 0.196 N
distance² = 3.39 x 10¹⁴ m²
Taking the square root of both sides, we find:
distance = √(3.39 x 10¹⁴ m²)
distance ≈ 5.82 x 10⁶ m
Therefore, the distance between the spheres is approximately 5.82 x 10⁶ meters.
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