Question

An insect is at the bottom of a hemispherical ditch of radius 1 m. 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)

Options

• 0.20 m

• 0.45 m

• 0.60 m

• 0.80 m

Answer 1

An insect is at the bottom of a hemispherical ditch of radius 1 m. 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 0.20 m.

Explanation:

Given: g = 10 ms⁻²

R = 1 m

At the point where the insect just starts slipping:

mg sin θ = μ mg cos θ

tan θ = μ

= 0.75

= `3/4`

cos θ = `4/5`

Relation between height and angle:

h = R(1 - cos θ)

= `1(1 - 4/5)`

= `1((5 - 4)/5)`

= `1(1/5)`

= 0.2 m