A mass of 5 kg is moving along a circular path of radius 1 m . If the mass moves with 300 rev/min , its kinetic energy would be

Options

A. `250 pi^(2)`
B. `100 pi^(2)`
C. `5 pi^(2)`
D. 0

Answer

A

Explanation

`m = 5 kg `
R=1 m
`omega = 300 `rev/min
` = (300 xx2pi)`rad/min
` = (300 xx2xx3.4) `rad/60 s
`= (300 xx 2xx 3.14)/60 ` rad/s = `10 pi` rad/s
Linear speed , `v = omega R`
`=(300xx2xx3.14)/60 " rad/s "10 pi `rad/s = `((300 xx2pi)/60)(1)`
= `10 pi ` m/s
`KE =1/2 mv^(2)`
` = 1/2 x5xx (10pi)^(2)`
` = 1/2 xx 5 xx (10pi)^(2)`
`= 250 pi^(2)` J