Question
Download Solution PDFThere are two identical spherical solid balls of iron alloy touching each other. What would be the gravitational force of attraction between them if the density of the materials of the ball is (3 /2π) × 105(kg/m3) and radius 1 m. G = 6.67 × 10-11Nm2/kg2.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe Correct answer is 0.667 N.
Key Points
- The gravitational force of attraction between two spherical solid balls can be calculated using Newton's law of gravitation, which is given by the formula: F = G * (m₁ * m₂) / d², where:
- G = Universal Gravitational Constant (6.67 × 10-11 Nm²/kg²).
- m₁ and m₂ are the masses of the two spheres.
- d is the distance between the centers of the spheres.
- To calculate the mass of each sphere, we use the formula for the volume of a sphere and multiply it by the given density:
- Volume of a sphere = (4/3)πr³ = (4/3) × π × (1 m)³ = (4/3)π m³.
- Density of the material is given as (3/2π) × 105 kg/m³.
- Mass of each sphere = Density × Volume = [(3/2π) × 105] × [(4/3)π] = 2 × 105 kg.
- Since the spheres are identical and touch each other, the distance between their centers is equal to twice the radius, i.e., d = 2 m.
- Substitute the values into the gravitational force formula:
- F = [6.67 × 10-11] × [(2 × 105) × (2 × 105)] / (2²).
- F = [6.67 × 10-11] × (4 × 1010) / 4.
- F = 0.667 N.
- Hence, the gravitational force of attraction between the two spheres is 0.667 N.
Additional Information
- Universal Gravitational Constant (G)
- G is a physical constant used in Newton's law of universal gravitation.
- Its value is approximately 6.67 × 10-11 Nm²/kg².
- The constant is essential for calculating the gravitational force between two masses.
- Henry Cavendish was the first to measure the value of G in 1798 using his torsion balance experiment.
- Density
- Density is defined as the mass per unit volume of a material.
- It is typically measured in units such as kg/m³.
- In this problem, the density of the spheres is given as (3 / 2π) × 105 kg/m³.
- Density is a key property in determining the mass of an object when its volume is known.
Last updated on Jul 8, 2025
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