A student proposes to measure the gravitational constant G by suspending two sph

Question

A student proposes to measure the gravitational constant G by suspending two spherical objects from the ceiling of a tall cathedral and measuring the deflection of the cables from the vertical. Draw a free-body diagram of one of the objects. (Do this on paper. Your instructor may ask you to turn in this work.)

If two 105.0 kg objects are suspended at the lower ends of cables 50.00 m long and the cables are attached to the ceiling 1.000 m apart, what is the deflection of each object? (Use 1.000 m for the separation distance in the expression for the gravitational force and assume that the deflection is extremely small compared to 1 m.)

Explanation / Answer

From the free body diagram of  the sphere

T sin() = F = G*m2/r2

T cos() = m*g

> tan()= G*m/(g*r2) = 7.14234 x 10-10

here  is small as F << mg 

 ---> tan()= 

deflection R*= 50*7.14234 x 10-10 = 3.571177 x 10-8 meters

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