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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassVariable massMedium2 minQB

PhysicsMediuminteger

A plane inclined at an angle 37° is covered with dust. An essentially massless dustpan on wheels is released from rest and rolls down the plane, gathering up dust. The density of dust in the path of the dustpan is $σ kg / m$ . What is the acceleration of the dustpan ?

Answer:

Solution:

Mass gathered after rolling $x$ : $m = σ x$ . Variable mass: $\frac{d ( m v )}{d t} = m g sin 3 7^{\circ}$ . $σ (x \frac{d v}{d t} + v^{2}) = σ xg sin 3 7^{\circ}$ . Constant acceleration: $v^{2} = 2 a x$ ⇒ $a x + 2 a x = xg sin 3 7^{\circ}$ . $a = \frac{10 \times 0.6}{3} = 2$ m/s $^{2}$

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Variable mass

⏱ 2mℹ️ Source: QB

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