Question

A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity `omega`. The tension in the strings is F. If the length of string and angular velocity are doubled, the tension in string is now ____________.

Options

• F

• `"F"/2`

• 4 F 

• 8 F

Answer 1

A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity `omega`. The tension in the strings is F. If the length of string and angular velocity are doubled, the tension in string is now 8 F.

Explanation:

Tension in string = centrifugal force

`"In first case, F" = "mr"omega^2`

`"In second case, F'" = "m"(2"r")(2omega)^2`

` = 8  "mr"omega^2`

`= 8  "F"`