particle P and Q are undeergoing uniform horizotal circular motion along concentric circle of different radii in clockwise sense . pcomplete each round in 2 min while q does in 5 min. time required by q to make one revolution around P
To find the time required by particle Q to make one revolution around particle P, we need to calculate the time taken for Q to travel the circumference of the circle on which P is moving.
The circumference of a circle can be calculated using the formula:
C = 2πr
Where C is the circumference and r is the radius.
Given that particle P completes each round in 2 minutes, and particle Q completes each round in 5 minutes, we can calculate the radii of the circles on which they are moving.
Let's assume the radius of the circle on which particle P is moving is rP, and the radius of the circle on which particle Q is moving is rQ.
Given that particle P completes each round in 2 minutes, we can write:
2πrP = 2 minutes
Simplifying this equation, we get:
rP = 2/(2π)
Similarly, given that particle Q completes each round in 5 minutes, we can write:
2πrQ = 5 minutes
Simplifying this equation, we get:
rQ = 5/(2π)
Now, to find the time required for particle Q to make one revolution around particle P, we need to calculate the circumference of the circle on which P is moving, and then divide it by the velocity of Q.
The circumference of the circle on which particle P is moving is 2πrP.
So, the time required for particle Q to make one revolution around particle P can be calculated as:
(Total distance travelled by Q) / (Velocity of Q)
= (2πrP) / (Velocity of Q)
= (2π * (2/(2π))) / (5 minutes)
= (2 * 2) / 5
= 4/5 minutes
Therefore, particle Q will take 4/5 minutes to make one revolution around particle P.