An object falling through a fluid is observed to have acceleration given by a = g – bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?
Correct option is A) If a spherical body of radius r is dropped in a viscous fluid, it is first accelerated and then its acceleration becomes zero and it attains a constant velocity called terminal velocity. According to the problem, acceleration of object is given by the relation a=g-bv When speed becomes constant acceleration a = dv/dt = 0 (uniform motion). where, g = gravitational acceleration Clearly, from above equation as speed increases acceleration will decrease. At a certain speed say v0, acceleration will be zero and speed will remain constant. Hence, a = g- bv0 = 0 ⇒ v0 = g/b
