Calculate the height upto which an insect can crawl up a fixed bowl in the from of a hemisphere of radius r Given coefficient of friction = 1 sqrt(3) .

Calculate the height upto which an insect can crawl up a fixed bowl in

1.	Calculate the height upto which an insect can crawl up a fixed bowl in the from of a hemisphere of radius r Given coefficient of friction = 1 sqrt(3) .
Answer» Solution :B is botton of the bowl of RADIUSR = OB . The insect can crawl up the bowl From B to P through a HEIGHT ` BA = h ` As is clear from ` R = W cos alpha ` and`F = W sin alpha ` where W is weight of insect and F is force of friction `mu = (F)/(R) = (Wsin alpha)/(W cos alpha) = TAN alpha (1)/(sqrt3) ` In ` triangleOPA , tan alpha = (PA)/(OA) ` `:. tan alpha = sqrt(r^(2) - Y^(2))/(y)= (1)/sqrt3 ` ` (r^(2) - y^(y))/(y^(2)) = (1)/(3) ` ` y^(2) = (3 r^(2))/(4) , y = (sqrt3 r)/(2) ` ` h = BA = OB = OB - OA = r - y ` ` h = r - (sqrt3 r )/(2) = 0 .134 r ` `h = 13 .4 %` of r.