A space-ship travelling in the interstellar medium is picking up dust& at a rate (dM)/(dt) = , where α is a positive constant,& v is the instantaneous velocity and& M & is the total mass of the space-ship at any

Correct answer: B. & - ^ 2 M (dM)/(dt) = F _ thrust = - v(dM)/(dt) = Ma ⇒ - v( ) = Ma ⇒ a = - ^ 2 M

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

NTA Abhyas 2020 · Physics · Center of Mass, Momentum and Collision

A space-ship travelling in the interstellar medium is picking up...

A space-ship travelling in the interstellar medium is picking up dust& at a rate $\dfrac{dM}{dt} = \alphav$ , where $\alpha$ is a positive constant,& $v$ is the instantaneous velocity and& $M$ & is the total mass of the space-ship at any instant.& The instantaneous acceleration of the space-ship& is

Options

A
& $\dfrac{− 2αv^{2}}{M}$
B
& $\dfrac{- \alphav^{2}}{M}$
C
& $\dfrac{− αv^{2}}{2M}$
D
$− \alphav^{2}$

Correct answer

& $\dfrac{- \alphav^{2}}{M}$

Step-by-step solution

$\dfrac{dM}{dt} = \alphav$

${F}_{thrust} = - v\dfrac{dM}{dt} = Ma$

$⇒ - v\left(\alphav\right) = Ma$

$⇒ a = - \dfrac{\alphav^{2}}{M}$

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