Question

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity `omega`. Two objects of mass m are attached gently to the opposite ends of diameter of the ring. The wheel will now rotate with angular velocity ______.

Options

• `(omega"M")/("M + m")`

• `(omega("M - 2m"))/("M + 2m")`

• `(omega"M")/("M + 2m")`

• `(omega("M + 2m"))/"M"`

Answer 1

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity `omega`. Two objects of mass m are attached gently to the opposite ends of diameter of the ring. The wheel will now rotate with angular velocity `(omega"M")/("M + 2m")`.

Explanation:

`"I"_"i" = "Mr"^2  "and"`

`"I"_"f" = ("M + 2m")"r"^2`

Now, according to law of conservation of angular momentum,

`"I"_"i"  omega_"i" = "I"_"f"  omega_"f"`

`therefore omega_"f" = ("Mr"^2omega)/(("M+2m")"r"^2`

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