Question

The work done by the frictional force on a surface in drawing a circle of radius r on the surface by a pencil of negligible mass with a normal passing force N (coefficient of friction Nuk) is:
(a) 4pi r^2 nu k N (b) -2pi r^2 nu k N (c)-2pi rnuk N (d) zero

Answer 1

Hey Mate

Solved it before. Photo from my notebook ✌✌✌✌

Brainliest

Answer 2

Hello friend,

It's a tricky question. You'll think displacement is zero so work done should be zero here, but trust me it's not.

◆ Answer- Option (C)

W = 2πrμkN

◆ Explaination-

Frictional force is given by-

Fk = μkN

At any point of time, work done by force F through minimal displacement ds is given by-

dW = -Fk.ds

For complete cycle, we'll take integration from ds=0 -> ds=2πr,

W = ʃdW

W = -ʃFk.ds

W = -ʃ(μkN).ds

W = -μkN ʃds

W = -μkN (2πr-0)

W = -2πrμkN

Therefore, total work done here is -2πrμkN .

Hope this is helpful...