A body covered a distance of `L m` along a curved path of a quarter circle. The ratio of distance to displacements.

Options

A. `pi//2 sqrt(2)`
B. `2sqrt(2)//pi`
C. `pi// sqrt(2)`
D. `sqrt(2)//pi`

Explanation

Length of quarter circle path = `L = 2pir//4`
` therefore r = 2L // pi`
Hence displacement AB ` = sqrt( r^(2) + r^(2)) = sqrt(2^(2))`.

From ` Delta OAB ` , magnitude of displacement = AB
` = sqrt(2^(r)) therefore (" Distance")/("Displacement ") = (2pir //4)/(sqrt 2.r) = pi//2 sqrt(2)`
Hence correct answer is (A)