Question

An exhausted house fly, mass 12mg, crusing with a speed of 2 m/s lands on a pool ball of mass 150g and radius of3 cm and immediately falls asleep. If the pool ball starts rolling without slipping, and if the rolling friction can be ignored, how long of a nap can the fly take before it is crushed as the ball rolls and carries the fly under it?

The moment of intertia of a solid sphere is I=2/5MR^2

Answer 1

Answer-As the linear momentum of the fly causes the pool ball to starts rolling so linear momentum of fly is converted into angular torque.so given M(fly)=12mg=0.012g and v=2m/s also R(radius of sphere)=3cm=0.03m M(mass of poll ball)=150g so,I=2/5*M(mass of poll ball)*R(radius of sphere)^2=2/5*150*(0.03)^2=0.054

NOW, M(fly)*v=I(moment inertia of sphere)*w(angular velocity)

0.012*2=0.054*w so,w=0.44m/s

now time taken when the fly gets crushed with sphere=2*pie*R(radius of sphere)/w=0.42s

so t=0.42s