Answer
a). When a disk rolls without slipping, the product $r\omega$ should be equal to $v_{CM}$. Hence, (2) equal to is correct.
b). For pure rolling, distance traveled by center of mass in rotating an angle of 2pi is equal to circumference i.e. $2pi\times r$.
Since $270^{\circ}$ corresponds to $\frac{3pi}{2}$ distance traveled by center of mass = $\frac{3pi}{2}\times\frac{2pi\times r}{2pi}=0.71m$
Since the given distance is equal to the calculated distance , the disk is rolling without slipping.
Work Step by Step
a). When a disk rolls without slipping, the product $r\omega$ should be equal to $v_{CM}$. Hence, (2) equal to is correct.
b). For pure rolling, distance traveled by center of mass in rotating an angle of 2pi is equal to circumference i.e. $2pi\times r$.
Since $270^{\circ}$ corresponds to $\frac{3pi}{2}$ distance traveled by center of mass = $\frac{3pi}{2}\times\frac{2pi\times r}{2pi}=0.71m$
Since the given distance is equal to the calculated distance , the disk is rolling without slipping.
