Question

A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the acceleration of the toy?a. g

b. 2πg
c. Zero
d. 4π²R/T²
e. πR/T²

Answer 1

d.
`(4\pi^(2) R)/(T^(2))`

Step-by-step explanation:

`R` = Radius of the circular path

`T` = Time period of motion

`w` = Angular speed of the motion

Angular speed of the motion is given as

`w = (2\pi )/(T)`

The toy is moving in a circle and hence centripetal acceleration acts on it which can be given as

`a = R w^(2) \\a = R ((2\pi )/(T))^(2)\\a = (4\pi^(2) R)/(T^(2))`

hence the correct choice is

d.
`(4\pi^(2) R)/(T^(2))`