The clay-turntable system's rotational inertia after strike will be (2/3)mR². Then the correct option is C.
<h3>What is rotational inertia?</h3>
The summation of the product of the mass of each particle with its square of the distance from the rotational axis is the moment of inertia, which is the amount denoted by the body resistant angular acceleration.
A turntable with mass m, radius R, and rotational inertia (mR²)/2 initially rotates freely about an axis through its center at constant angular speed with negligible friction.
A piece of clay, also of mass m, falls vertically onto the turntable and sticks to it at point P, a distance R/2 from the center of rotation.
Then the clay-turntable system's rotational inertia after strike will be

More about the rotational inertia link is given below.
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I think it’s clumped distribution
Explanation:
The frictional resistance of the various pipes are given by the
K value in the table which may be used with the formula
hf = KQ2
to relate the magnitude of head loss hf in the pipeline
to the volumetric flow rate, Q. Water is drawn at the constant flow
rates from the network at nodes C and D. The static heads
(elevation + pressure head) at nodes B, C and D are 100m, 65m
and 61m respectively above the local datum. Calculate the
discharges at C and D and the water level in reservoir A. (The
data has been added to the diagram to aid the solution)
Use no more than 3 iterations and 3 significant figures.