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Q.

An insect is at the bottom of a hemispherical ditch of radius 1m. It crawls up the ditch but starts slipping after it is at height ‘h’ from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then ‘h’ is: $(g = 10 m s^{- 2})$

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a

0.60 m

b

0.45 m

c

0.20 m

d

0.80 m

answer is C.

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$\begin{array}{l} A t a p o i n t w h e r e s l i p p i n g j u s t s t a r t s, \\ f = m g \sin θ \\ \Rightarrow μ m g \cos θ = m g \sin θ \\ \Rightarrow \tan θ = μ \\ a s μ = 0.75, θ = 37^{0} \\ ∴ h = R (1 - \cos θ) = 0.20 m \end{array}$

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An insect is at the bottom of a hemispherical ditch of radius 1m. It crawls up the ditch but starts slipping after it is at height ‘h’ from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then ‘h’ is: g=10 ms−2