Question

A particle of mass $m$ is made to move with uniform speed $v$ along the perimeter of a regular hexagon. Magnitude of impulse applied at each corner is:

• A. $mv$
• B. $mv\sqrt{3}$
• C. $\frac{mv}{2}$
• D. $\frac{mv}{\sqrt{3}}$

Answer 1

The correct option is A $mv$

Let at first it has only one component $v$ after a turn of ${120}^0$. It has two components $\frac{v}{2}$ and $\frac{\sqrt{3}v}{2}$

so the change in velocity is $(v-\frac{v}{2})\hat{i}+\frac{\sqrt{3}v}{2}\hat{j}$

Total change in velocity $=\sqrt{\frac{v^2}{4}+\frac{{3v}^2}{4}}=v$

Total cange in momentum i.e., impulse $=mv$