CBSE Class 9 Answered

Find the ratio of distance travelled and displacement of the particle in a semicircle of radius r.

Asked by Topperlearning User | 09 Jun, 2016, 02:47: PM

Expert Answer

$begin mathsize 12px style Displacement space equals space Straight minus line space distance space AB space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space Diameter space of space circle space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 straight r space space space space space space space space space space space space space space space space space space space space space Distance equals space Actual space length space of space path space ACB space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space circumference space of space semi minus circle space space space space space space space space space space space space space space space space space space equals space 1 half space circumference space of space circle Since space the space circumference space of space straight a space circle space of space radius space straight r space equals space 2 πr Distance space travelled space equals space 1 half space 2 πr space equals space straight pi Therefore comma space Distance over Displacement space equals space fraction numerator space πr over denominator 2 straight r end fraction space equals space fraction numerator space straight pi over denominator 2 end fraction end style$