Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms–1. How long does the body take to stop?
A man of mass 70 kg stands on a weighing scale in a lift which is moving
- upwards with a uniform speed of 10 m s-1
- downwards with a uniform acceleration of 5 m s–2
- upwards with a uniform acceleration of 5 m s–2. What would be the readings on the scale in each case?
- What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?
A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)
An empty plastic box of mass m is found to accelerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?
Let m1 = 1 kg, m2 = 2 kg and m3 = 3 kg in the following figure. Find the accelerations of m1, m2 and m3. The string from the upper pulley to m1 is 20 cm when the system is released from rest. How long will it take before m1 strikes the pulley?
Write the mathematical form of Newton's second law of motion. State the conditions if any.
A body of mass 5 kg is moving with velocity 2 m s-1. Calculate its linear momentum.
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.
How long will a stone take to fall to the ground from the top of a building 80 m high
A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g = 10 m s-2 and speed of sound = 330 m s-1. Find : The time when echo is heard after the pebble is dropped.
A body of mass 200 g is moving with a velocity of 5 ms−1. If the velocity of the body changes to 17 ms−1, calculate the change in linear momentum of the body.
What do you understand by the term momentum?
State Newton's second law of motion. Is Newton's first law of motion contained in Newton's second law of motion?
State Newton's second law of motion.
A body of mass 400 g is resting on a frictionless table. Find the acceleration of the body when acted upon by a force of 0.02 N.
A stone is dropped from a tower 98 m high. With what speed should a second stone be thrown 1 s later so that both hit the ground at the same time?
What do you mean by the conservation of momentum? Briefly, explain the collision between two bodies and the conservation of momentum.
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
Why is catching a slow-moving ball easier than catching a fast-moving ball?
