Question

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A body complete 31/2 revolution around the circle of radius r is 7cm. calculate the velocity of the body, if the time taken to complete one revolution is 5sec.

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Answer 1

Answer:

Given:

31/2 revolution = 15 full and ½ revolution completed around a circle of radius 7 cm.

Time taken to complete one revolution is 5 seconds.

To find:

Velocity of the body.

Concept:

Velocity is the ratio of displacement to the time taken.

So for 15 revolutions, the displacement will be zero as the starting and ending point is same.

Displacement for last ½ revolution is 2r.

Calculation:

Hence displacement = 2r

=> displacement = 2 × 7

=> displacement = 14 cm.

Time taken for 15 and ½ revolution is

= 5 × 15 + 5/2

= 75 + 2.5

= 77.5 seconds.

Hence average Velocity

= displacement/time

= 14/(77.5)

= 0.1806 cm/seconds.

So final answer is

$\boxed{avg. \: velocity = 0.1806 \: cm \: {s}^{ - 1}}$

Answer 2

Answer:

$\large\boxed{\sf{1.8 \times {10}^{ - 3} \: m {s}^{ - 1} }}$

Explanation:

Given that, a body completes 31/2 revolution around the circle .

Radius of the circle , r = 7 cm

Total revolution = $\dfrac{31}{2}= \dfrac{(30+1)}{2}= 15 + \dfrac{1}{2}$

Time taken to Complete one revolution = 5 sec.

.°. Total time taken, t = (5 × 15)+(5 × ½)

= 75 + 5/2

= 155/2 sec.

Now, To find the velocity, we know that,

• $\sf{Velocity(v)=\dfrac{Displacement(d)}{Time(t)}}$

We have displacement for complete 15 revolution = 0

And, displacement of ½ revolution = 2r = 14 cm = 0.14 m

Therefore, we have,

$\implies v = \frac{14 \times {10}^{ - 2} }{ \frac{155}{2} } \\ \\ \implies \: v = \frac{28 \times {10}^{ - 2} }{ 155} \\ \\ \implies \: v = 0.18 \times {10}^{ - 2} \\ \\ \implies \: v = 1.8 \times {10}^{ - 3} \: m {s}^{ - 1}$