Question

The minute hand of a clock is 5 cm long. Calculate the distance covered and the
displacement of the minute hand of the clock from 3AM to 3.30AM

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{Displacement \ is \ 15.62 \ cm}$

$\bold\blue{Explanation}$

The length of minute hand is 5 cm,

while moving it will create an imaginary arc.

This arc will be equal to Displacement.

$\bold\orange{Given:}$

Minute hand= 5 cm

$\bold\pink{To \ find:}$

Displacement of minute hand from 3 am to 3.30 am.

$\bold\green{\underline{\underline{Solution}}}$

$\bold{=>Difference \ between \ 3 \ am \ and \ 3.30 \ am}$

$\bold{is \ half \ an \ hour. }$

$\bold{One \ full \ rotation \ of \ minute \ hand}$

$\bold{is \ equal \ to \ one \ hour.}$

$\bold{Full \ rotation=360° }$

$\bold{One \ hour=360° }$

$\bold{Half \ an \ hour=\frac{360}{2}}$

$\bold{Half \ an \ hour=180° }$

$\bold{Formula \ for \ length \ of \ arc=\frac{thita}{360} × 2r × \pi }$

$\bold{Length \ of \ arc= \frac{180}{360}×2×\frac{22}{7}×5}$

$\bold{=> Length \ of \ arc=\frac{22}{7}×5}$

$\bold{=> Length \ of \ arc=15.62 \ cm.}$

Therefore,

$\bold\purple{Displacement \ is \ 15.62 \ cm}$