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Chapter 13: Q.40 - Excercises And Problems (page 354)

Two100kglead spheres are suspended from 100-m-long massless cables. The tops of the cables have been carefully anchored exactly 1mapart. By how much is the distance between the centers of the spheres less than 1m?

Short Answer

Expert verified

the distance between the centers of the spheres is1.4脳10-5m

Step by step solution

01

Given information

mass of sphere 1is m1=100kg

mass of sphere 2is m2=100kg

Length of the cableL=100m

02

Explanation

The gravitational force F=Gm2r2=mgtan胃tan胃=Gm2gr2

Distance change on each side is Lsin胃

so, the total distance is ,S=2Lsin胃

For small angle we have,

sin胃=tan胃=胃

The above equation can be written as

role="math" localid="1649926341518" S=2Lsin胃=2L胃S=2LGm2gr2=2脳100脳6.67脳10-11脳1002=9.8脳(1)2=1.4脳10-5m

So, the distance between the centers of the spheres is1.4脳10-5m

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