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NEET PHYSICSEasy

Sand is being dropped on a conveyor belt at the rate of M kg/sM \text{ kg/s}. The force necessary to keep the belt moving with a constant velocity of v m/sv \text{ m/s} will be:

A

MvMv N

B

2Mv2Mv N

C

Mv2\frac{Mv}{2} N

D

Zero

Step-by-Step Solution

  1. Concept: According to Newton's Second Law of Motion, the net force acting on a body is equal to the rate of change of its momentum (F=dpdtF = \frac{dp}{dt}) [NCERT Class 11, Physics Part I, Sec 5.5].
  2. Variable Mass System: Here, the mass is changing with time, but the velocity is constant. The momentum p=mvp = mv. F=d(mv)dt=mdvdt+vdmdtF = \frac{d(mv)}{dt} = m\frac{dv}{dt} + v\frac{dm}{dt}
  3. Application:
  • Since the velocity vv is constant, acceleration dvdt=0\frac{dv}{dt} = 0.
  • The rate of change of mass is given as dmdt=M kg/s\frac{dm}{dt} = M \text{ kg/s}.
  • Therefore, the term mdvdtm\frac{dv}{dt} vanishes, leaving: F=v(dmdt)=v⋅M=Mv NF = v \left( \frac{dm}{dt} \right) = v \cdot M = Mv \text{ N}
  1. Conclusion: The force required to maintain constant velocity is MvMv newton.
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