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STD 11 - 4.1. newtons laws of motion — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 4.1. newtons laws of motion4 Marks
MCQ
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{ dM ( t )}{ dt }= bv ^{2}( t ),$ where $v ( t )$ is its instantaneous velocity. The instantaneous acceleration of the satellite is
  • A
    $-\frac{2 b v^{3}}{M(t)}$
  • B
    $-\frac{ bv ^{3}}{2 M ( t )}$
  • C
    $-b v^{3}(t)$
  • ✓
    $-\frac{b v^{3}}{M(t)}$
✓

Answer

Correct option: D.
$-\frac{b v^{3}}{M(t)}$
d
$\frac{\operatorname{dm}( t )}{ dt }= bv ^{2}$

$F _{\text {thast }}= v \frac{ dm }{ dt }$

Force on statellile $=-\overrightarrow{ v } \frac{ dm ( t )}{ dt }$

$M ( t ) a =- v \left( bv ^{2}\right)$

$a = - \frac{ bv ^{3}}{ M ( t )}$

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