There 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.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 0.667 N.
- 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:
- Where,
- G = Universal Gravitational Constant (6.67 10 -11 * Nm 2 / 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 sphere volume formula and multiply it by the given density:
- Volume of a sphere = (4/3)πr³ = (4/3) × π × (1 m)³ = (4/3)ㅠm³.
- 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 = 2m
- 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 = 0.667N .
Hence, the gravitational force of attraction between the two spheres is 0.667N.