Question

A particle is travelling in a circle of diameter 15 m. Calculate the distance covered and displacement when it completes 2 rounds. ​

Answer 1

Answer:

Given:

• Diameter of the circle = 15 m.

To find:

Distance covered and displacement when it completes two rounds.

Solution:

We know that perimeter of a circle = 2πr

So distance covered when it completes two rounds = 2 × 2πr

= 4 × 3.14 × 7.5

= 94.2 m

Total distance covered will be 94.2 m and total displacement will be 0 because it comes back to the initial point after completing two rounds.

Answer 2

Required Question :-

A particular is travelling in a circle of diameter 15m calculate the distance covered and displacement when it completes 2rounds

Given :-

• Diameter = 15 cm.

Solution :-

We know that,

$\\ \: \: \: \: \underline{ \boxed{ \color{navy}\sf \: The \: circumference \: of \: circle \: = \: πd \: }}$

$\\ \: \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \pi \times diameter$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf \: Put \: the \: values \:$

$\\ \: \sf \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \frac{22}{7} \times 15$

$\\ \: \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \frac{330}{7}$

$\sf \: \: \: \therefore \: distance \: covered \: in \: 2 \: rounds$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: : \: \implies \: 2 \times circumference$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: : \: \implies \: 2 \times \frac{330}{7}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: : \: \implies \: \frac{660}{7}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: : \: \implies \: \boxed{ \pink{\frak{94.3 \: meters}}}$

$\: \: \: \sf \underline{ Displacement = 0 \: metre \: [ \: since \: the \: particles \: returns \: to \: origin. ] }$

The total distance covered is 94.3 metres.

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