Question

A pair of scissors is used to cut a wire of circular cross section held vertically. To reduce required force the wire must be placed close to the hinge; but if it is placed close to the hinge, it slides away from the hinge until the angle between the blades becomes $\theta$. Find the coefficient of friction between the blades and the wire.

• A. $cot\left(0.5\theta \right)$
• B. $\tan \left(0.5\theta \right)$
• C. $0.5\tan \theta$
• D. Insufficient information

Answer 1

The correct option is B $\tan \left(0.5\theta \right)$

$f-$ frictional force

$f=\mu N$

As shown in fig;

$f\cos \frac{\theta }{2}=Nsin\frac{\theta }{2}$

$\mu =\tan \frac{\theta }{2}=\tan \left(0.5\theta \right)$

Option B is correct.