Thus, statement $(a)$ is correct.
As the body is rotating, its instantaneous acceleration is not zero.
Hence, statement $(b)$ is incorrect.
Once perfect the rolling begins, force of friction becomes zero. Hence, work done against friction is zero.
Thus, statement $(c)$ is correct.
Rolling cannot take place in the absence of friction because it is the frictional force that provides the necessary torque which makes the body roll on a surface. When the inclined plane is perfectly smooth, the wheel will simply slip under the effect of its weight.
Hence, statement $(d)$ is correct.
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$(A)$ $R \propto n ^{1 / 3}$ and $v \propto n ^{2 / 3}$
$(B)$ $R \propto n ^{2 / 3}$ and $v \propto n ^{1 / 3}$
$(C)$ $E=\frac{3}{2}\left(\frac{n^2 h^2 F^2}{4 \pi^2 m}\right)^{1 / 3}$
$(D)$ $E=2\left(\frac{n^2 h^2 F^2}{4 \pi^2 m}\right)^{1 / 3}$