Question

A balloon has 2g of air. A small hole is pierced into it. The air comes out with a velocity of $4m/s$. If the balloon shrinks in 2.5s. The average force acting on the balloon is
A. 0.0008N
B. 0.0032N
C. 8N
D. 3.2N

Answer 1

Hint: To solve this question define the force in terms of the momentum and time. Again, momentum can be expressed in terms of mass and velocity. put the given values on the obtained expression to get the required answer.

Complete answer:
The mass of the air inside the balloon is, $m=2g=0.002kg$.
The velocity of the air coming out of the balloon through the small hole is, $v=4m/s$
The balloon shrinks or the time required for the gas to completely come out of the balloon is, $t=2.5s$
We need to find the average force on the balloon.
From Newton’s second law, we know that the force on an object can be defined as the rate of change of momentum. In general, mathematically we can express it as,
$F=\dfrac{P}{t}$
Where, F is the force, P is the change in momentum and t is the time.
Now, the momentum of an object can be defined as the product of the mass and the velocity of the object. Mathematically we can write it as,
$P=mv$
Where, m is the and v is the velocity of the object.
Putting the expression for the momentum on the expression for force, we will get,
$F=\dfrac{mv}{t}$
Putting the given values on the above expression we can get the force on the balloon.
$F=\dfrac{0.002\times 4}{2.5}=0.0032N$
So, the force on the balloon is $0.0032N$

The correct option is (B).

Note:
Momentum is a physical term that defines the quantity of motion of an object. The linear momentum can be simply expressed as the product of the mass and velocity. The Newton’s laws of motion relate an object's motion with the force acting on it.