A sand dropper drops sand of mass m(t) on a c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The power $P$ required to maintain a constant speed $v$ for a conveyor belt onto which mass is being dropped is given by $P = F \cdot v$.Since the

Vedclass · Accepted Answer

$P^2 \propto v^5$

Vedclass · Answer

(D) The power $P$ required to maintain a constant speed $v$ for a conveyor belt onto which mass is being dropped is given by $P = F \cdot v$.Since the belt moves at a constant speed,the force $F$ required to overcome the momentum change of the added sand is $F = \frac{dp}{dt} = v \frac{dm}{dt}$.Given that the rate of mass deposition is $\frac{dm}{dt} = k\sqrt{v}$,where $k$ is a constant.Substituting this into the force equation: $F = v(k\sqrt{v}) = kv^{3/2}$.Now,calculating the power: $P = F \cdot v = (kv^{3/2}) \cdot v = kv^{5/2}$.Squaring both sides of the equation,we get $P^2 = k^2 v^5$.Therefore,$P^2 \propto v^5$.

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

Similar Questions

$A$ cart loaded with sand is moving with velocity $v$. Sand is falling through a hole as shown in the diagram. After falling on the ground,the sand is:

$A$ rocket with an initial mass $m_0$ is going up with a constant acceleration $a$ by exhausting gases with a velocity $v$ relative to the rocket motion. The mass of the rocket at any instant of time $t$ is (assume that no other forces act on it).

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/s^2$. If after $5 \,s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be.........$m$

If the force on a rocket having an exhaust velocity of $300 \, m/s$ is $210 \, N$,then the rate of combustion of the fuel is ........... $kg/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module