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NEET 2026
Exam
NEET
Year
2026
Subject
Physics
Chapter
Chapter

NEET 2026 · Physics · Chapter

A stationary satellite in deep space suddenly ruptures into three...

A stationary satellite in deep space suddenly ruptures into three distinct modules due to an internal failure. The modules have masses MM, 2M2M, and 3M3M. The module of mass MM is ejected along the positive x-axis with a speed of 120 m/s120 \text{ m/s}, while the module of mass 2M2M is ejected along the positive y-axis with a speed of 80 m/s80 \text{ m/s}. What is the speed of the heaviest module?

Options

  1. A200 m/s200 \text{ m/s}
  2. B1003 m/s\dfrac{100}{3} \text{ m/s}
  3. C2803 m/s\dfrac{280}{3} \text{ m/s}
  4. D2003 m/s\dfrac{200}{3} \text{ m/s}

Correct answer

D. 2003 m/s\dfrac{200}{3} \text{ m/s}

Step-by-step solution

Initial momentum of the satellite is zero.

By conservation of linear momentum:

P⃗1+P⃗2+P⃗3=0\vec{P}_1 + \vec{P}_2 + \vec{P}_3 = 0

The momentum of the first module is P⃗1=M(120i^)=120Mi^\vec{P}_1 = M(120 \hat{i}) = 120M \hat{i}.

The momentum of the second module is P⃗2=2M(80j^)=160Mj^\vec{P}_2 = 2M(80 \hat{j}) = 160M \hat{j}.

Let the velocity of the heaviest module of mass 3M3M be v⃗\vec{v}. Its momentum is P⃗3=3Mv⃗\vec{P}_3 = 3M \vec{v}.

Substituting the values:

120Mi^+160Mj^+3Mv⃗=0120M \hat{i} + 160M \hat{j} + 3M \vec{v} = 0

3Mv⃗=−120Mi^−160Mj^3M \vec{v} = -120M \hat{i} - 160M \hat{j}

v⃗=−40i^−1603j^\vec{v} = -40 \hat{i} - \dfrac{160}{3} \hat{j}

The speed of the heaviest module is the magnitude of its velocity:

∣v⃗∣=(−40)2+(−1603)2|\vec{v}| = \sqrt{(-40)^2 + \left(-\dfrac{160}{3}\right)^2}

∣v⃗∣=1600+256009|\vec{v}| = \sqrt{1600 + \dfrac{25600}{9}}

∣v⃗∣=14400+256009|\vec{v}| = \sqrt{\dfrac{14400 + 25600}{9}}

∣v⃗∣=400009=2003 m/s|\vec{v}| = \sqrt{\dfrac{40000}{9}} = \dfrac{200}{3} \text{ m/s}

Answer: 2003 m/s\dfrac{200}{3} \text{ m/s}
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