A wheel makes 360 revolutions in 1 minute. Through how many radians does it turn in 3 seconds?a)6πb)36πc)10πd)12πCorrect answer is option 'B'. Can you explain this answer?

Question

A wheel makes 360 revolutions in 1 minute. Through how many radians does it turn in 3 seconds?a)6&#960;b)36&#960;c)10&#960;d)12&#960;Correct answer is option 'B'. Can you explain this answer?

Answer

The wheel makes 360 revolutions in 1min=360revolutions/1min=360revolutions/60seconds=6revolutions/1sec
=18revolutions/3sec
For one revolution the circle is turned by an angle of 2πradians.
For 18revolutions it makes 18*2πradians =36πradians.

Answer

In 1 min it makes 360 revolutions That means in 60 sec _ 360 revolution So, in 3 seconds it makes 18 revolution Now W = 2pi V W=2pi ×18 =36pi

Answer

To find out how many radians the wheel turns in 3 seconds, we need to convert the given information into radians per second.

Given:
- The wheel makes 360 revolutions in 1 minute.
- There are 60 seconds in 1 minute.

Converting revolutions per minute to radians per second:
- There are 2π radians in one revolution.
- So, the wheel makes 360 * 2π radians in 1 minute.
- To find the radians per second, we divide this by 60 (seconds per minute).
- Therefore, the wheel makes (360 * 2π) / 60 radians per second.

Calculating the radians turned in 3 seconds:
- Now, we need to find out how many radians the wheel turns in 3 seconds.
- To do this, we multiply the radians per second by the number of seconds.
- So, the wheel turns [(360 * 2π) / 60] * 3 radians in 3 seconds.

Simplifying the expression:
- [(360 * 2π) / 60] * 3
- (6π) * 3
- 18π

Therefore, the wheel turns 18π radians in 3 seconds.

Now, let's check which option matches our answer:
a) 6 radians - Not the correct answer.
b) 36 radians - Not the correct answer.
c) 10 radians - Not the correct answer.
d) 12 radians - Not the correct answer.

None of the given options match our answer of 18π radians. Therefore, the correct answer is not provided in the given options.

Answer

B is correct

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