A house is built on the top of a hill with `45^(@)`slope Due to the sliding of meterial and sand top from top to the bottom of till , the slip angle has been redaced if the coefficient of static friction between sand particles is `0.75` what is the final angle attated by bill ? `(tan^(-1) 0.75= 37^(@))`

Options

A. `8^(@)`
B. `45^(@)`
C. `37^(@)`
D. `30^(@)`

Answer

c

Explanation

As sand particles are sliding down , the slope of the hill gets radaced The sand particle slope coming down when component of gravity force along the hill is balanced by limiting friction force
`mg sin theta = mu_(s) mg cos theta`
`rArr theta = tan^(-1) (mu_(s)) = 37^(@)`
where `theta` is the new slope angle of half.