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 ?

Explanation

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 momentum change (Impact),
`F_(1)=mR sqrt(2gh)`, force due to weight `F_(2)= mg`. Rt
`therefore` Total reading,
`F=mgRt+mR sqrt(2gh)=mg R(t+sqrt((2h)/(g)))`