Question

If a body takes time t to complete one round of the circular path of radius r, then the speed of the body (v) is given by

a. v = πr × t

b. v = πr/t

c.2πr/t

d. 2πr × t

Answer 1

Answer:

$\huge\boxed{\sf{\red{c. \; \dfrac{2\pi r}{t}}}}$

Explanation:

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

• Time taken by body to complete one round of the circular path = t
• Radius of the circular path = r

We've been asked to calculate speed of the body i.e, v.

As we know that,

$\mapsto \boxed{ \sf{ Speed = \dfrac{Distance}{Time} }}$

We have the value of time that is t, given in the question. We need to find the distance travelled first.

As the body covers one round of the circular path, hence distance travelled will be the total length of the circular path or basically, circumference of the circular path will be the distance travelled that is, $\boxed{\sf{ 2 \pi r}}$.

Hence,

$\mapsto \boxed{ \sf{\red{ v = \dfrac{2 \pi r}{t}} }}$

Therefore, speed of the body is 2πr/t. Option C is correct.

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Answer 2

Explanation:

Given :-

If a body takes time t to complete one round of the circular path of radius r,

To Find :-

Speed of the body (v)

Solution :-

We know that

If a body covers one round of circle then it covers the circumference of the circle.

We know that

Circumference of circle = 2πr

Given, radius = r

=> Distance = 2πr

Now,

=> Time taken = t

Also, we know that

=> Speed = Distance/Time

=> Speed (v) = 2πr/t

=> v = 2πr/t

Option C is correct