Question

If the speed of uniform circular motion of the body is reduced by 5 times and the radius of the circle is increased by 3 times, then how and how many times will the centripetal acceleration change?

Answer 1

Step-by-step explanation:

Centripetal acceleration of a body in uniform circular motion is given by the formula a = v^2/r, where v is the speed of the body and r is the radius of the circle.

If the speed of the body is reduced by 5 times, then its new speed will be 1/5th of the original speed, i.e., v' = v/5.

If the radius of the circle is increased by 3 times, then its new radius will be 3 times the original radius, i.e., r' = 3r.

Using the formula for centripetal acceleration, we can find the new acceleration as follows:

a' = (v'/r')^2

= (v/5)/(3r))^2

= (v^2/225r)

Therefore, the centripetal acceleration will be reduced by 225 times (1/225 of the original acceleration).

Answer 2

The centripetal acceleration of a body undergoing uniform circular motion is governed by the formula a = v^2/r, where v is the speed of the body and r is the radius of the circle.

Now, if the speed of the body is reduced by 5 times, its new speed becomes v/5, where v represents the original speed. Likewise, the radius of the circle increases by 3 times, with the new radius being represented by 3r, where r is the original radius.

Upon plugging these values into the formula for centripetal acceleration, we arrive at:

a' = (v/5)^2/(3r) = v^2/(75r)

Therefore, the centripetal acceleration experiences a decrease of 75 times in comparison to its original value. This decline occurs as a result of the reduced speed and the increased radius of the circular motion.