A simple accelerometer is constructed inside a car by sus$-$pending an object of mass m from a string of length L that is tied to the car$$s ceiling. As the car accelerates the string$$object system makes a constant angle of u with the vertical. $($a$)$ Assuming that the string mass is negligible compared with m$,$ derive an expression for the car$$s acceleration in terms of u and show that it is independent of the mass m and the length L$.($b$)$ Determine the acceleration of the car when u $523\mathrm{.}0.$