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A balloon has 5gm of air. A small hole is pierced 
into it, the air escapes at a uniform rate with a 
velocity of 4cm/sec. If the balloon shrinks completely 
in 2.5 second, the mean force acting on the balloon is
  • a)
    2 dynes
  • b)
    50 dynes
  • c)
    8 dynes
  • d)
    8 N
Correct answer is option 'C'. Can you explain this answer?
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A balloon has 5gm of air. A small hole is piercedinto it, the air esca...
Given data:
Mass of air in the balloon = 5 gm
Velocity of air escaping = 4 cm/sec
Time taken for balloon to shrink completely = 2.5 sec

To find: Mean force acting on the balloon

The force acting on the balloon can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum.

𝐹 = 𝑚𝑎

Where,
F = Force (to be determined)
m = Mass of air in the balloon
a = Acceleration

Since the velocity is given in cm/sec, we need to convert it to m/sec.

Given velocity = 4 cm/sec
Converting to m/sec: 4 cm/sec * (1 m/100 cm) = 0.04 m/sec

The acceleration can be calculated using the formula:

a = 𝑣/𝑡

Where,
v = Velocity of air escaping
t = Time taken for balloon to shrink completely

Substituting the values:
a = 0.04 m/sec / 2.5 sec = 0.016 m/sec²

Now substituting the values of mass and acceleration into the equation F = ma:

F = 5 gm * 0.016 m/sec² = 0.08 N

Therefore, the mean force acting on the balloon is 0.08 N, which is equivalent to 8 dynes. So, option C is the correct answer.
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