Two gear wheels, A and B, start from rest and accelerate uniformly. Wheel A attains a rotational speed of 600 rpm in 10 s , while wheel B attains a rotational speed of 900 rpm in 12 s . The ratio of the angular acceleration of wheel A to that of wheel B is

Step-by-step solution

Let _A and _B be the angular accelerations of wheels A and B respectively. Since both start from rest, the angular acceleration is given by = t . For wheel A: _A = 600 rpm , t_A = 10 s . _A 600 10 = 60 For wheel B: _B = 900 rpm , t_B = 12 s . _B 900 12 = 75 The ratio of their angular accelerations is: _A _B = 60 75 = 4 5 . The conversion factor from rpm to rad s ⁻¹ cancels out in the ratio. Answer: 4:5