An insect is at the bottom of a hemi spherical ditch of radius 1m. It crawls up the ditch but starts slipping after it is at a 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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0.60 m

0.45 m

0.20 m

0.80 m

answer is A.

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Detailed Solution

Here $N = m g \cos θ, f = μ N = μ m g \cos θ$

Insect will start slipping if $m g \sin θ \geq f$

$m g \sin θ \geq μ m g \cos θ$

$\tan θ \geq μ$

For limiting value , $\tan θ = μ = 0.75$

$h = R - R \cos θ = 1 - 1 \times \frac{4}{5} = 0.20 m$

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