Question

For this part, imagine that the string is wound around the center axle of a yo-yo; the axle radius is Raxle, but the yo-yo casing has a radius Rcasing≫Raxle and moment of inertia I≫mr2axle. In the limit the moment of inertia of the yo-yo I→[infinity] and the mass m of the yo-yo remains finite, what magnitudes would you expect for the tension T in the vertical section of string and the downward acceleration a of the center of mass? Choose the option that best describes the limiting values of T and a under the conditions given. Choose the option that best describes the limiting values of and under the conditions given.

A T=0 and a=0
B T=[infinity] and a=0
C T=mg and a=0
D T=[infinity] and a=g
E T=0 and a=[infinity]
F T=[infinity] and a=[infinity]

Answer 1

When the moment of inertia tends to infinity and the mass remains finite, the limiting values of tension and acceleration are T=mg and a=0 respectively.

Step-by-step explanation:

When the moment of inertia (I) of the yo-yo tends to infinity and the mass (m) remains finite, the tension (T) in the vertical section of the string and the downward acceleration (a) of the center of mass can be determined. In this case, the limiting values of T and a are given by option C: T = mg and a = 0.

The tension in the vertical section of the string is equal to the weight of the yo-yo, which is mg due to gravity.

Since the moment of inertia (I) tends to infinity, the rotational motion of the yo-yo is negligible, resulting in no acceleration (a=0) of the center of mass.

Answer 2

The limiting values of the tension T and downward acceleration a in the given scenario are T=mg and a=0.

Step-by-step explanation:

In the given scenario, where the moment of inertia of the yo-yo approaches infinity and the mass remains finite, the limiting values of the tension T in the vertical section of the string and the downward acceleration a of the center of mass would be:

T = mg (Option C)

a = 0 (Option B)

As the moment of inertia becomes infinite, the tension in the string becomes equal to the weight of the yo-yo, which is mg. Since the yo-yo is not accelerating vertically, the downward acceleration of the center of mass is zero.