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An insect crawls up a hemispherical surf...

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 `alpha` with the vertical, the maximum possible value of `alpha` is given by

A

`cotalpha=3`

B

`tan alpha=3`

C

`sec alpha=3`

D

`cosec alpha =3`

Text Solution

Verified by Experts

The correct Answer is:
A
`N= mg cos alpha` ,br> `:.f= mu N=mu mg cos alpha`

and `f=mu N=mg sin alpha`
`:.mu mg cos alpha=mg sin alpha`
`implies cot alpha=(1)/(mu)=3`
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Knowledge Check

  • An insect craws up a hemispherical surface very slowly (see fig.). The coefficient of friction between the insect and the surface is 1//3 . If the line joining the center of the hemispherical surface to the insect makes an angle alpha with the vertical, the maximum possible value of alpha is given by

    A
    `cot alpha=3`
    B
    `tan alpha=3`
    C
    `sec alpha=3`
    D
    `cosec alpha=3`

  • The coefficient of friction between an insect and a hemispherical bowl of radius r is mu . The maximum height to which the insect can crawl in the bowl is

    A
    `( r )/( sqrt( 1+ mu^(2)))`
    B
    `r[1-(1)/( sqrt( 1+ mu^(2)))]`
    C
    `r sqrt( 1+ mu^(2))`
    D
    `r[ sqrt( 1+ mu^(2))-1]`

  • A force of 100N is applied on a block of mass 3kg as shown in the figure. The coefficient of friction between the surface and the block is mu=(1)/(sqrt(3) . The friction force acting on the bock is.

    A
    15N downward
    B
    25N upward
    C
    20N downword
    D
    30N upward