Question

A cyclist goes around circular track ones every 2min with 5.5m/sec find the radius​

Answer 1

Appropriate Question:

A cyclist goes around circular track once every 2 min with 5.5 m/s. Find the radius.

Answer:

105 m

Explanation:

As per the provided information in the given question, we have :

• Time taken to cover 1 round of the circular track = 2 minutes
• Speed attained = 5.5 m/s

We've been asked to calculate the radius of the circular track.

In order to calculate the radius of the circular track, firstly we'll calculate the circumference of the track. Now the question arises that how would we find the circumference of the track, basically, here circumference of the track is the distance covered by the body in one round. We've been provided with the speed and time taken. So, by applying a suitable formula we can find the distance covered by the body in one round that is the circumference of the track.

Before commencing the steps, firstly we need to convert time taken into minutes.

$\longrightarrow \sf{\quad {t= 2\; minutes }}$

Multiply 2 with 60 to convert 2 minutes into seconds as 1 minute consists of 60 seconds.

$\longrightarrow \sf{\quad {t= (2 \times 60)\; s }}$

$\longrightarrow \quad \boxed{\sf{t= 120 \; s }}$

Let's denote circumference by C.

$\longrightarrow \sf{\quad {C = Distance \; Covered }}$

• Distance = Speed × Time

$\longrightarrow \sf{\quad {C = Speed \times Time }}$

$\longrightarrow \sf{\quad {C = \Big ( 120 \times 5.5\Big ) \; m }}$

$\longrightarrow \quad \boxed{\sf{ C= 660 \; m }}$

Now, as we know that,

$\bigstar \quad \underline{\boxed{ \pmb{\frak{ C = 2 \pi r }} }}$

• r denotes radius

$\longrightarrow \sf{\quad {660 = 2 \times \dfrac{22}{7} \times r }}$

$\longrightarrow \sf{\quad {660 = \dfrac{44}{7} \times r }}$

$\longrightarrow \sf{\quad {660 \times 7= 44 \times r }}$

$\longrightarrow \sf{\quad {4620= 44 \times r }}$

$\longrightarrow \sf{\quad {\cancel{\dfrac{4620}{44}}= \times r }}$

$\longrightarrow \quad \underline{\boxed{ \pmb{\frak{ 105 \; m = r }} }}$

Therefore, radius of the circular track is 105 m.