Question

A body coverd a distance of 2 metre along a semicular path.calculate the magnitude of displacement of the body, and the ratio of distance to displacement

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Distance covered (s) = 2m
• Body covered semicircular path.

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Displacement
• Ratio of Distance and Displacement

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For semicircular path -

$\color{violet}\underline{\boxed{\sf Distance=πr}}$

$\implies{\sf 2=3.14×r}$

$\implies{\sf r=\dfrac{2}{3.14}}$

$\color{orange}\implies{\sf r = 0.6m }$

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❏ Displacement

Shortest Distance Travelled by the body is refered to as Displacement.

here ,

Displacement = 2R

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 × 0.6

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\color{red}\implies{\sf 1.2\:m}$

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❏ Ratio of Distance and Displacement

Distance = 2m

Displacement = 1.2m

$\implies{\sf \dfrac{Distance}{Displacement}=\dfrac{2}{1.2}}$

$\color{red}\implies{\sf \dfrac{Distance}{Displacement}={0.95}}$

$\color{darkblue}\underline{\underline{\sf Answer -}}$

Displacement = $\color{red}{\sf 1.2m}$

Ratio of Distance and Displacement = $\color{red}{\sf 0.95}$.

Answer 2

Answer:

Let R be the radius of the circle

Displacement in a semi circular path = 2R

Distance covered in semi circular path = πR

Ratio of distance covered to displacement = π/2