A satellite in force free space sweeps stationary interplanetary dust at a rate of dM/dt = α v , where M is mass and v is the speed of satellite and α is a constant. The acceleration of satellite is

Question

A satellite in force free space sweeps stationary interplanetary dust at a rate of dM/dt = α v , where M is mass and v is the speed of satellite and α is a constant. The acceleration of satellite is (A)  (- α v2/2M) (B) - α v2 (C)  (- 2α v2/M) (D)  (- α v2/M)

Tardigrade Admin · Accepted Answer

Rate of change of mass (d M/d t)=α v. Retarding force = Rate of change of momentum = Velocity × Rate of change in mass =-v × (d M/d t) =-v × α v=-α v2. (Minus sign of v due to deceleration) Therefore Acceleration =(-α v2/M).

Q. A satellite in force free space sweeps stationary interplanetary dust at a rate of $d M / d t = αv$ , where $M$ is mass and $v$ is the speed of satellite and $α$ is a constant. The acceleration of satellite is

$\frac{- α v ^{2}}{2 M}$

$- α v^{2}$

$\frac{- 2 α v ^{2}}{M}$

$\frac{- α v ^{2}}{M}$

Rate of change of mass $\frac{d M}{d t} = αv$ .
Retarding force $=$ Rate of change of momentum
$=$ Velocity $\times$ Rate of change in mass $= - v \times \frac{d M}{d t}$
$= - v \times αv = - α v^{2}$ .
(Minus sign of $v$ due to deceleration)
Therefore Acceleration $= \frac{- α v ^{2}}{M}$ .

Q. A satellite in force free space sweeps stationary interplanetary dust at a rate of dM/dt=αv , where M is mass and v is the speed of satellite and α is a constant. The acceleration of satellite is

2M−αv2​

−αv2

M−2αv2​

M−αv2​