Question

A balloon has mass of 10 g in air The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s If the balloon shrinks in 5 s completely Then, the average force acting on that balloon will be (in dyne)

• A. 3
• B. 9
• C. 12
• D. 18

Answer 1

The Correct Option is B

To determine the average force acting on the balloon, we need to apply the basic principles of momentum and force. Here's the step-by-step solution:

1. Identify Given Values:
   • Mass of the balloon, m = 10 \, \text{g} = 0.01 \, \text{kg} (since 1 g = 0.001 kg).
   • Velocity of air escaping, v = 4.5 \, \text{cm/s} = 0.045 \, \text{m/s} (since 1 cm = 0.01 m).
   • Time during which air escapes, t = 5 \, \text{s}.
2. Calculate Change in Momentum:
   • The change in momentum (\Delta p) is given by the product of the mass of the balloon and the velocity of the escaping air:
   • \Delta p = m \cdot v = 0.01 \, \text{kg} \times 0.045 \, \text{m/s} = 0.00045 \, \text{kg m/s}.
3. Calculate Average Force:
   • Using the formula for force (F = \frac{\Delta p}{\Delta t}), where \Delta t is the time interval, we find the average force:
   • F = \frac{0.00045 \, \text{kg m/s}}{5 \, \text{s}} = 0.00009 \, \text{N}.
4. Convert Force to Dyne:
   • Since 1 Newton is equal to 10^5 dyne:
   • F = 0.00009 \, \text{N} \times 10^5 \, \text{dyne/N} = 9 \, \text{dyne}.

Thus, the average force acting on the balloon is 9 dyne, which corresponds to the correct option 9.