Question

A particles semicircular path of radius r. The ratio of distance travelled and displacement of particle will be:

Answer 1

Answer:

Given:

Particle travels semicircle ( half of a circle).

To find:

Ratio of distance to displacement

Concept:

Distance is the total path length traversed by a body.

Displacement is the shortest length between starting and stopping point

Calculation:

For a semicircle :

$\star \: \sf{distance = \dfrac{2\pi r}{2}}$

$\sf{ \star \: displacement \: = 2r}$

See the diagram to understand better .

Hence ratio :

$\sf{distance \: : displacement}$

$\sf{ = \pi r : 2r}$

$\sf{ = \pi : 2}$

So final answer :

$\boxed{ \bold { \red{ \sf{ ratio = \pi : 2}}}}$

Answer 2

$\blue{\underline{ \huge{ \blue{\boxed{ \mathfrak{\fcolorbox{red}{orange}{\purple{Answer}}}}}}}} \\ \\ \star \rm \: \blue{Given} \\ \\ \leadsto \rm \: a \: particle \: moves \: on \: semicircle \: of \\ \rm \: radius \: r \: from \: a \: to \: b \\ \\ \star \rm \: \blue{To \: Find} \\ \\ \leadsto \rm \: ratio \: of \: distance \: travelled \: by \: \\ \rm \: particle \: and \: displacement \\ \\ \star \rm \: \blue{Concept} \\ \\ \dagger \rm \: \boxed{ \red{ \rm{Distance}}} \implies \rm \: the \: total \: length \\ \rm \: of \: path \: that \: is \: covered \: by \: particle \: \\ \rm is \: called \: as \: distance... \\ \leadsto\rm \: here \: distance = \frac{perimeter}{2} = \pi{r} \\ \\ \dagger \: \boxed{ \rm{ \red{Displacement}}} \implies \rm \: the \: shortest \\ \rm \: distance \: between \: two \: points \: is \: called \\ \rm \: as \: displacement... \\ \leadsto \rm \: here \: displacement = 2r \\ \\ \star \rm \: \blue{Calculation} \\ \\ \leadsto \rm \: \frac{Distance}{Displacement} = \frac{\pi{r}}{2r} = \frac{\pi}{2} \\ \\ \dagger \: \underline{\boxed{ \bold{ \rm{ \orange{ratio = \pi {:2} }}}}} \: \dagger$