Cricket bats are designed to efficiently transfer energy to the ball, hitting it from the 'sweet spot' where the bat experiences pure rotational motion about the grip. From its handle end, find the sweet spot, $x_{s}$, of the cricket bat shown in the figure. The linear mass density of the bat can be described by $(0.56 + 3.6x^2)$ kg/m, with $x$ in meters from the handle end. The total length of the bat is 1.2 m. The optimal point for rotation should be 15 cm from the handle end. Hint: Consider where the center of mass of the bat might be located.