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

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

is

: \left(g = 10m{s}^{- 2}\right) An insect is at the bottom of a hemispherical ditch of radius 1m . It crawls up the ditch but starts slipping after it

Options

A $0 . 20m$
B $0 . 45m$
C $0 . 60m$
D $0 . 80m$

Correct answer

A. $0 . 20m$

Step-by-step solution

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

$mgsin\theta = \mu mgcos\theta$

$tan\theta = \mu = 0 . 75$

$⇒ \theta = 37$

$cos\theta = \dfrac{R - h}{R}$

$\cos 37 = \dfrac{1 - h}{1} ⇒ h = 0 . 2$

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