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Marbles each of mass'm' are dropped from...

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 ?

Text Solution

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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)=mgR(t+sqrt((2h)/(g)))`
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