Marbles each of mass 'm' are dropped from height 'h' on pan of a balance at the rate 'R' per sec. The balance calibrated in units of mass reads zero initially. If marbles are dropped continuously, what will the balance read after 't' sec ?

Marbles each of mass 'm' are dropped from height 'h' on pan of a balan

1.	Marbles each of mass 'm' are dropped from height 'h' on pan of a balance at the rate 'R' per sec. The balance calibrated in units of mass reads zero initially. If marbles are dropped continuously, what will the balance read after 't' sec ?
Answer» Solution :Each marble hits the pan with VELOCITY `v=sqrt(2gh)`and in 1 sec no. of marbles hitting the pan = R `therefore` Force due to momentumchange (Impact), `F_(1)=MR sqrt(2gh)`, force due to weight `F_(2)=` mg. Rt `therefore` TOTAL reading, `F=mgRt + mR sqrt(2gh)=mgR(t+sqrt((2h)/(g)))`