can an object be in pure translation as well as in pure rotation?
No, an object cannot be in pure translation as well as in pure rotation at the same time. Pure translation means the object is moving in a straight line without any rotation, while pure rotation means the object is rotating about a fixed axis without any translational motion. These two types of motion are mutually exclusive, and an object can only have one type of motion at a time.
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is : 
Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by $\frac{x{256} Mr^2$. The value of x is ___.