Friction is a force that aids us daily, in fact so much so that we don't even pause to appreciate its important. We would not be able to wear pants or jeans without friction. We would have to live like aborigines in the jungle. The shirt is supported at our shoulders. But if we stand up the weight of our jeans is to be supported by a verticle force. The surface of our shoulders. But if we stand up the weight of our jeans is to be supported by a vertical cylinder. The force of friction acting between this curved surface and jeans balances the weight of the jeans. To understand this mathematically, let us consider a verticle man whose waist is a rigid cylinder having a circumference of 90 cm. He wears a jeans of mass 500 gm using an elastic massless belt which can be assumed to be on elastic string of forc e constant `500N//m` and circumference 85cm when not extended. The coefficient of friction between waist and jeans is `0.5`. What is the friction force acting between the man's waist and jeans?

Options

A. 5 N
B. `12.5 N`
C. `7.5 N`
D. 25 N

Answer

A

Explanation

FBD of jeans
`dN=Tdtheta`
Max. value of friction
`f_(max)=intmudN`

`f_(max)=underset0overset(2pi)(int) muTd theta(T=kx=500xx.05=25N)`
`f_(max)=2pimuT=2pixx.5xx25=78.5398 N`
force acting downward is force of gravity `=mg=5N(downarrow)`
static force of friction is self adjustable in nature therefore friction will be 5N(upward)