Physics quiz question: hammer throw chain length

Physics 205A Quiz 5, fall semester 2016
Cuesta College, San Luis Obispo, CA

"2010 Asian Games - Men's Hammer Throw Final"
cctv7military
youth.be/DGsuBw0A-r8

The "hammer" used in a hammer throw competition can be approximated[*] as a ball spun in a circle at the end of a chain of negligible mass, with a rotational speed of 24 rad/s. The rotational inertia of the ball and chain system is 11 kg·m². (I_{point mass} = m·r².) If the mass of the ball is 7.3 kg, the length of the chain is:
(A) 0.66 m.
(B) 1.2 m.
(C) 1.5 m.
(D) 2.2 m.

[*] wired.com/2012/08/olympics-physics-hammer-throw/

Correct answer (highlight to unhide): (B)

The rotational inertia of a point mass m and moving in a circle of radius r is:

I_{point mass} = m·r²,

such that solving for the radius (which would be the length of the chain):

r² = I_{point mass}/m,

r = √(I_{point mass}/m),

r = √((11 kg·m²)/(7.3 kg)) = 1.227537907792867 m,

or to two significant figures, the chain length is 1.2 m.

(Response (A) is m/I_{point mass}; response (C) is √(m·g/I_{point mass}); response (D) is m·g/I_{point mass}.)

Sections 70854, 70855, 73320
Exam code: quiz05b0oM
(A) : 4 students
(B) : 32 students
(C) : 14 students
(D) : 5 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38