Advertisements
Advertisements
Question
The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall to the earth's surface with a constant velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v?
Advertisements
Solution
Let M be mass of the balloon.
Let the air resistance force on balloon be F .
Given that F ∝ v.
⇒ F = kv,
where k = proportionality constant.
When the balloon is moving downward with constant velocity,
B + kv = Mg ...(i)
\[\Rightarrow M = \frac{B + kv}{g}\]
Let the mass of the balloon be M' so that it can rise with a constant velocity v in the upward direction.
B = Mg + kv
\[\Rightarrow M' = \frac{B + kv}{g}\]
∴ Amount of mass that should be removed = M − M'.
\[∆ M = \frac{B + kv}{g} - \frac{B - kv}{g}\]
\[ = \frac{B + kv - B + kv}{g}\]
\[ = \frac{2kv}{g} = \frac{2\left( Mg - B \right)}{g}\]
\[ = 2\left\{ M - \frac{B}{g} \right\}\]
APPEARS IN
RELATED QUESTIONS
The below figure shows the position-time graph of a particle of mass 4 kg.
- What is the force on the particle for t < 0, t > 4 s, 0 < t < 4 s?
- What is the impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only.)
Consider the situation shown in the following figure All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.
In the previous problem, suppose m2 = 2.0 kg and m3 = 3.0 kg. What should be the mass m, so that it remains at rest?
Calculate the tension in the string shown in the following figure. The pulley and the string are light and all the surfaces are frictionless. Take g = 10 m/s2.
The unit of linear momentum is :
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : Change in momentum of the body.
A bullet of mass 50 g moving with an initial velocity 100 m s-1 strikes a wooden block and comes to rest after penetrating a distance 2 cm in it. Calculate: (i) Initial momentum of the bullet, (ii) Final momentum of the bullet, (iii) Retardation caused by the wooden block and (iv) Resistive force exerted by the wooden block.
State the magnitude and direction of the force of gravity acting on the body of mass 5 kg. Take g = 9.8 m s-2.
An electron of mass 9 × 10−31 kg is moving with a linear velocity of 6 × 107 ms−1. Calculate the linear momentum of electron.
A motorcycle of mass 100 kg is running at 10 ms−1. If its engine develops an extra linear momentum of 2000 Ns, calculate the new velocity of a motorcycle.
What do you understand by the term momentum?
Multiple Choice Question. Select the correct option.
A force acts on a body of mass 3 kg such that its velocity changes from 4 ms−1 to 10 ms−1. The change in momentum of the body is
ame the law of motion which gives the definition of force.
What causes motion in a body?
Name the physical quantity which equals the rate of change of linear momentum.
What do you mean by an impulsive force?
The INCORRECT statement about Newton's second law of motion is
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is ______.
Why is catching a slow-moving ball easier than catching a fast-moving ball?
How does moving your hand backward while catching a cricket ball reduce pain?
