A satellite moving with velocity v in a force | vedclass

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

Question

(B) According to Newton's second law,the net external force $F$ acting on a system is equal to the rate of change of momentum: $F = \frac{d}{dt}(Mv)$.

Vedclass · Accepted Answer

$-\frac{\alpha v^2}{M}$

Vedclass · Answer

(B) According to Newton's second law,the net external force $F$ acting on a system is equal to the rate of change of momentum: $F = \frac{d}{dt}(Mv)$.Since the satellite is moving in force-free space,the external force $F = 0$.Therefore,$\frac{d}{dt}(Mv) = 0$.Expanding this using the product rule: $M \frac{dv}{dt} + v \frac{dM}{dt} = 0$.We are given the rate of mass collection as $\frac{dM}{dt} = \alpha v$.Substituting this into the equation: $M \frac{dv}{dt} + v(\alpha v) = 0$.Rearranging to solve for acceleration $a = \frac{dv}{dt}$:$M a + \alpha v^2 = 0$.$M a = -\alpha v^2$.$a = -\frac{\alpha v^2}{M}$.

$A$ satellite moving with velocity $v$ in a force-free space collects stationary interplanetary dust at a rate of $\frac{dM}{dt} = \alpha v$,where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is:

Similar Questions

Sand is being dropped on a conveyor belt at the rate of $M \ kg/s$. The force necessary to keep the belt moving with a constant velocity of $v \ m/s$ will be

In the first second of its flight,a rocket ejects $1/60$ of its mass with a velocity of $2400\,m/s$. The acceleration of the rocket is ............ $m/s^2$.

$A$ rocket motor consumes $100 \ kg$ of fuel per second,exhausting it with a speed of $5 \ km/s$. The speed of the rocket when its mass is reduced to $\frac{1}{20}$ of its initial mass is (Assume initial speed to be zero and ignore gravitational and viscous forces.)

$A$ rocket of initial mass $6000 \ kg$ ejects gases at a constant rate of $16 \ kg/s$ with a constant relative speed of $11 \ km/s$ in gravity-free space. What is the acceleration of the rocket $1 \ min$ after the blast? (in $m/s^2$)

$A$ rocket is ejecting $50\,g$ of gases per second at a speed of $500\,m/s.$ The accelerating force on the rocket will be ............ $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module