Motion Of An Insect In The Rough Bowl - Practice Questions & MCQ

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $1 / 3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\theta$ with the vertical, the maximum possible value of $\theta$ is given by

If the coefficient of friction between on insect and bowl is $\mu$ and the radius of the bowl is r . Find the maximum height to which insect can crawl up in the bowl.

An insect is at the bottom of a hemisphere 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 $\mathrm{b} / \mathrm{w}$ the ground and insect is 0.75 . Then h is : $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

A block of mass $m$ is placed on a surface having vertical cross section given by $y=x^2 / 4$. If coefficient of friction is 0.5 , the maximum height above the ground at which block can be placed without slipping is:

An inclined plane is bent in such a way that the vertical cross-section is given by $y=\frac{x^2}{4}$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu=0.5$, the maximum height in cm at which a stationary block will not slip downard is $\qquad$ cm.

If the coefficient of friction between insect and bowl is $\mu$ and the radius of the bowl is $r=\sqrt{3} \mathrm{~m}$. If the maximum height to which the insect can crawl up in the bowl is $h=r-y_{\text {the }}$ the value of y is -$\left(\mu=\frac{1}{-3}\right)$

An insect trapped in circular groove. If it completes its 20 revolutions in 1 min with constant speed then frequency of insect is :