An insect crawling up a fixed hemispherical bowl of radius .R. If the coefficient of friction is 13, then the insect can only crawl upto a height of

See fig.The insect will crawl up the bowl till the component of its weight down the plane just equals the force of limiting frictionF=Wsin⁡α  and  N=Wcos⁡αμ=tan⁡α=F/N=1/3 But tan⁡π2−α=cot ⁡α=xR2−x2 so that  X=3/10=0⋅949RNow  h=R−x=0⋅051R.