Question

A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity:

विकल्प

• `omega (("M" + 2"m"))/"M"`

• `omega (("M" - 2"m"))/(("M" - 2"m"))`

• `(omega"M")/("M" - 2"m")`

• `(omega"M")/("M" + 2"m")`

Answer 1

`(omega"M")/("M" + 2"m")`

Explanation:

Since no torque on the system

∴ Angular momentum remains constant.

i.e., `"L"_"initial" = "L"_"final"` or `"I"omega = "I'"omega"'"`

or, `"MR"^2 omega = ("MR"^2 + 2 "MR"^2)`ω'

`therefore omega"'" = ("MR"^2 omega)/("R"^2 ("M" + 2"m")) = (omega "M")/("M" + 2"m")`

Therefore the ring will now rotate with an angular velocity `= (omega "M")/(("M" + 2"m"))`