Question

The work done by the frictional force on a pencil in drawing a complete circle of radius r = $1/\pi$ metre on the surface by a pencil of negligible mass with a normal pressing force N = 5 N ($\mu =0.5$) is

• A. + 4J
• B. -3 J
• C. -2 J
• D. -5 J

Answer 1

The correct option is D -5 J

Given: a pencil in drawing a complete circle of radius $r=\frac{1}{\pi }$ metre on the surface by a pencil of negligible mass with a normal pressing force N = 5 N ($\mu$=0.5)

To find the work done by the frictional force on a pencil

Solution:

Let the frictional force applied be $\overrightarrow{F_k}$

$\overrightarrow{F_k}$ acts tangentially opposite to the motion of the pencil.

For elementary displacement $\overrightarrow{dl}$,

The work done by $\overrightarrow{F_k}$ is $dw$

So $dw=\overrightarrow{F_k}.\overrightarrow{dl}=-F_{k}dl$

Integrating on both side, we get

$w=-{\int }_0^{2\pi r}{F}_k.dl⟹w=-{\mu }_{k}N{\int }_0^{2\pi r}dl⟹w=-{\mu }_{k}N\times 2\pi r$

Here given, $r=\frac{1}{\pi },N=5N,{\mu }_k=0.5$

Substituting these value in the above equation, we get

$w=-\left(0.5\right)\times 5\times 2\times \pi \times \frac{1}{\pi }⟹w=-5J$

is the work done by the frictional force on a pencil in drawing a complete circle.