A mass is supported on a frictionless horizontal surface. It Is attached to a string and rotates about a fixed center at an angular velocity `omega_(0)`.If the length of the string and angular velocity both are doubled, the tension in the string which was initially `T_(0)` is now

Options

A. `T_(0)`
B. `T_(0)//2`
C. `4T_(0)`
D. `8T_(0)`

Answer

D

Explanation

`T = momega^(2)r`
`T_(0) = momega_(0)^(2) r_(0)`
`T = m(2omega_(0))^(2) (2r_(0)) = 8momega_(0)^(2)r_(0) = 8T_(0)`