Work Energy Power

JEE Main level, single correct, medium

145 of 183

Question 145 of 183

A sand dropper drops sand of mass m(t)m(t) on a conveyer belt at a rate proportional to the square root of speed (v)(v) of the belt, i.e. dmdt∝v\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

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Answer: (C) P2∝v5\mathrm{P}^2 \propto v^5

Power =F⃗⋅V⃗=\vec{F} \cdot \vec{V}
and F=dpdt=F=\frac{d p}{d t}= Rate of change of linear momentum
F=V⋅dmdt=K1V32,KF=V \cdot \frac{d m}{d t}=K_1 V^{\frac{3}{2}}, K is constant
Power (P)=(KV32)⋅(V)(P)=\left(K V^{\frac{3}{2}}\right) \cdot(V)
=KV52=K V^{\frac{5}{2}}

So, P2∝V5P^2 \propto V^5

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