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_(t) = mR sqrt(2gh)`, force fue to weight `F_(2)= mg.RT`
`therefore` Total reading.
F = mgRt + mR`sqrt(2gh) = mgR(t + sqrt((2h)/g))`