A simple accelerometer is constructed inside a car by suspending 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 θ 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 θ and show that it is independent of the mass m and the length L. (b) Determine the acceleration of the car when θ = °.