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Two spheres of equal size and equal mass are rotated with an equal amount of torque. One of the spheres is solid with its mass evenly distributed throughout its volume, and the other is hollow with all of its mass concentrated at the edges. Which sphere would rotate faster?(A) Solid sphere(B) Hollow sphere(C) They would rotate at equal rates.(D) Additional information is required to determine the relative rates of rotation.

A

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Chapter 1

Practice Test 1

Section 1

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here we have two spheres, one of which is hollow and other is solid and both have same radius and masks. So we have to find out the rate of rotation if both are both are subjected to the same talk. So for hollow sphere moment of inertia is let us say I won two by three mass M are square. R radius and mass is um for solid is fair moment of inertia is I do two x 5 M. R Square. No angular acceleration is alpha equal to dark by a moment of inertia. No we can clearly see that. I won Sorry I two is less than I one so the late of rotation which depends on angular acceleration will be faster for the solid sphere. We can also find out by finding out the angular acceleration for hollow sphere is dark which is same for both. It's fierce. So talk by island Dark is dull and I want is to buy three M. R. Square. This gives us three Dow by to um are square. This is rate of rotation that is angular acceleration for Hollow sphere and for solid sphere. Fatto is powered by two quilted Dabei two by five M. R. Square. This gives us five dog by to M. R. Square. So Clearly Alpha two is greater than Alpha one. So that's all it is feared will rotate faster. Uh huh. Hence the correct option is a. This completes the solution. Thank you.

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