In case of variable mass what will be the general equation of force?

F = M a

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F = \frac{M d v}{d t} + \frac{v d M}{d t}

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F = \frac{M d v}{d t} + \frac{v d M}{d t} - \frac{u d M}{d t}

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\frac{u d M}{d t}

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Solution

The correct option is A $F = \frac{M d v}{d t} + \frac{v d M}{d t} - \frac{u d M}{d t}$
Since the actual velocity will be $v_{a c t .} = v - u$ , $P = M (v - u)$ Applying Newton's second law,

$F = \frac{d P}{d t} = \frac{d (M (v - u))}{d t}$

$F = M \frac{d v}{d t} - M \frac{d u}{d t} + v \frac{d M}{d t} - u \frac{d M}{d t}$

SInce velocity of conveyer belt is constant, $\frac{d u}{d t} = 0$

Hence, $F = M \frac{d v}{d t} + v \frac{d M}{d t} - u \frac{d M}{d t}$

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