Question : Sand is being dropped on a conveyer belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity if v m/s will be
a) Mv/2 Newton
b) Zero
c) Mv Newton
d) 2Mv Newton
[AIPMT, 2008]
Doubt by Manasvini
Solution :
This is problem of variable mass system, it means the mass is not constant but it changes with time.
As per Newton's Second Law of Motion—
The rate of change of linear momentum is equal to the external force applied.
F=dp/dt
F=d(mv)/dt [∵p=mv]
F=v(dm/dt) [As per the question velocity (v) need to be constant, so it can be taken out of differentiation]
F=vM [∵dm/dt =M(Given in the Question)]
This is problem of variable mass system, it means the mass is not constant but it changes with time.
As per Newton's Second Law of Motion—
The rate of change of linear momentum is equal to the external force applied.
F=dp/dt
F=d(mv)/dt [∵p=mv]
F=v(dm/dt) [As per the question velocity (v) need to be constant, so it can be taken out of differentiation]
F=vM [∵dm/dt =M(Given in the Question)]
F=Mv
Hence, the required force that would be necessary to keep the belt in motion would be Mv Newton.
So, c) would be the correct option.