(a) Starting with the mathematical expression for the gravitational force between two…

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

(a) Starting with the mathematical expression for the gravitational force FF between two point masses m1m_1 and m2m_2 separated by a distance rr, obtain an equation in the form log⁡F=C−2 log⁡r,\log F = C - 2\,\log r, where CC is a constant for a given pair of masses. (b) Hence prove that a graph of log⁡F\log F (vertical axis) versus log⁡r\log r (horizontal axis) is a straight line and determine its slope. (c) The following experimental data were collected for a fixed pair of small spheres: (r/m): 1.0,  2.0,  4.0\bigl(r/\text{m}\bigr):\,1.0,\;2.0,\;4.0; (F/N): 10.0,  2.50,  0.625\bigl(F/\text{N}\bigr):\,10.0,\;2.50,\;0.625. Using any two convenient pairs of data, calculate the slope of the straight line that would pass through the corresponding points on a log⁡F\log F versus log⁡r\log r graph and comment on its agreement with the theoretical value obtained in part (b).

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