The acceleration of gravity g can be determined by measuring the time t it takes for a mass m₂ in an Atwood’s machine to fall a distance L, starting form rest.

(a) Find an expression for g in terms of m₁, m₂, L, and t.

(b) Show that if there is a small error in the time measurement dt, it will lead to an error in the determination of g by an amount dg given by dg/g = –2 dt/t/ If L = 3 m and m₁ is 1 kg, find the value of m₂ such that g can be measured with an accuracy of ±5% with a time measurement that is accurate to 0.1 s. assume that the only significant uncertainty in the measurement is the time of fall.