Question

a person moves on a circular path of 10m his displacement after two and half revolution will be

25 m

50 m

20 m

10 m​

Answer 1

Need to FinD :-

• The displacement of person after two and half revolutions .

$\red{\frak{ Given}}\begin{cases} \textsf{ A person moves on a circular path of radius 10m}\\\textsf{ He makes two and a half revolutions .}\end{cases}$

Firstly we know that the Displacement is the shortest distance between any two points . Here a person is moving on a track of radius 10m. So when he makes 2 and a half revolutions starting from a point say A then after 2 revolutions he will be on same Point A . And after completing another half revolution he will move to another point say B which is located at the straight line passing through centre O .

Now here we will have two distances , out of which the shortest one will be the Displacement . Here , the first distance is A to B through the boundary of circle . This distance will be equal to half the circumference . That is ,

$\sf:\implies \widehat{AB} = \dfrac{2\pi r}{2}\\\\\sf:\implies \widehat{AB} = \pi r \\\\\sf:\implies \widehat{AB} = 3.14 \times 10m \\\\\sf:\implies \boxed{\pink{\frak{ \widehat{AB} = 31.4 m }}}$

Now the second distance will be the diameter AOB . This is equals to 2 times the radius .

$\sf:\implies \overline{AOB } = 2r \\\\\sf:\implies \overline{AOB } = 2(10m) \\\\\sf:\implies \boxed{\pink{\frak{ \overline{AOB} = 20m }}}$

Therefore we see that out of the two distances second one is less. Therefore the Displacement is 20m .