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Properties of Matter question

2022 · 28 Jul · Shift 1 · Q50
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  5. /2022 · 28 Jul · Shift 1 · Q50

Properties of Matter question

2022 · 28 Jul · Shift 1 · Q50

JEE MainPhysicsProperties of MatterMCQ+4 / −1
A balloon has mass of 10 g10 \mathrm{~g}10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s4.5 \mathrm{~cm} / \mathrm{s}4.5 cm/s. If the balloon shrinks in 5 s5 \mathrm{~s}5 s completely. Then, the average force acting on that balloon will be (in dyne).
  1. A
    3
  2. B
    9
  3. C
    12
  4. D
    18
View written solutionFree

Correct answer: B

  1. Given data
  • Initial mass of balloon (with air): m=10 gm = 10\text{ g}m=10 g
  • Air escapes with speed: u=4.5 cm/su = 4.5\text{ cm/s}u=4.5 cm/s
  • Balloon becomes empty in: t=5 st = 5\text{ s}t=5 s

We need the average force on the balloon due to escaping air.

  1. Use rocket-thrust idea

If mass is expelled at rate dmdt\dfrac{dm}{dt}dtdm​ with relative speed uuu, then thrust magnitude is F=udmdtF = u\frac{dm}{dt}F=udtdm​

Since the air escapes uniformly, the mass loss rate is constant.

  1. Compute mass loss rate

The whole 10 10\,10g of air/mass is lost in 5 5\,5s, so dmdt=105=2 g/s\frac{dm}{dt} = \frac{10}{5} = 2\text{ g/s}dtdm​=510​=2 g/s

  1. Compute force

F=udmdt=4.5×2=9F = u\frac{dm}{dt} = 4.5 \times 2 = 9F=udtdm​=4.5×2=9

In CGS units: g⋅cm/s2=dyne\text{g·cm/s}^2 = \text{dyne}g⋅cm/s2=dyne

So, F=9 dyneF = 9\text{ dyne}F=9 dyne

  1. Check options
  • A: 333 dyne
  • B: 999 dyne
  • C: 121212 dyne
  • D: 181818 dyne

Hence, the correct option is B.

  1. Comparison with stored answer

Stored correct answer: B

Our derived answer: B

They match.

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