I've been mega busy with something for past several weeks, so much so that I nearly forgot that a world exists around me and there is a great deal to think and do other than what I was busy with. When I came out of the trance (when a friend called me up to inquire whether I still exist in the same world as his or have been transported to the mars over the floo network !), I brought my mind back to the natural games of the world. Let me share a random thought or two which came to me after I touched the earth again.
Answer this in one-thirtieth of a minute. In my room, I have two different objects kept on the two pans of a simple balance. On what factors does the inclination of the balance depend? a. Mass of each of the two objects (or the difference thereof) b. Shape of each of the two objects c. Composition of each of the two objects. d. It is written
Your time is up. So what is it? a. Mass of each of the two objects. Sure?
confident?
phone a friend?
should i lock it?
Come on, think over it again. If it is on Ankit's blog it can't be such trivial a thing! If your answer is a, I am going to disprove you in the next couple of minutes.
Actually, it depends on how we define the mass of an object, or, how we define the object itself! Thinking in a trivial way, I would say, the mass of an object is the mass of everything contained within it; irrespective of what the composition is. I'll make it simple now. I'll give you an example where I keep objects of same mass on the two pans of the balance, but the balance would still be inclined on one side.
I have a hollow tennis ball. How do you calculate the total mass of a hollow ball? It is the mass of the shell, plus the mass of the air inside it. Fair enough, right? Now, let's have a similar ball on the other pan. Both balls would weigh the same. The balance will be at equilibrium. Now, let the second ball start shrinking. Let it shrink to half the diameter of the original. Mind it, we've just shrunk the ball, not changed its mass. The ball simply gets denser. The air inside it gets compressed. The overall mass of the ball remains the same. But you will see the balance tilting to the side of this ball, suggesting that this ball is actually becoming heavier. The more you shrink it, the more is the weight as suggested by the balance. So, now we have two balls, of equal mass, on both sides of the balance. And the balance suggests that one of them is heavier. Is it not absolutely strange?
I know you won't take my word for it. So, I will tell you the logical reason behind this. (wow!! when I write sentences like this, it makes me feel like a really educated person, so ignorant and naive though I am ! ). Actually, what acts upon the balance pans apart from the ball's weight is the pressure of air. The atmospheric pressure. Air pressure is nothing but the weight of the air column directly above the pans (consider a cylinder of air with one end on the pan and the other at the end of atmosphere, the weight of air in that cylinder acts on the pan). In the case of the first ball with uncompressed air, what acted upon the pan was the weight of the shell of the ball, plus the air pressure (the weight of the air inside the ball is accounted for, as it is a part of the air column which applies air pressure). In case of the second ball, since we have compressed some air, there is more air in the air column pressing this pan. So, there is a bit more air, plus the shell of the ball, hence the total force on the second pan will be higher. Hence, the balance tilts towards the second pan.
So, you know, things are not that simple. And as I told you had this thing been simple, or uninterestingly complex, it wouldn't be there on my blog!
Answer this in one-thirtieth of a minute. In my room, I have two different objects kept on the two pans of a simple balance. On what factors does the inclination of the balance depend? a. Mass of each of the two objects (or the difference thereof) b. Shape of each of the two objects c. Composition of each of the two objects. d. It is written
Your time is up. So what is it? a. Mass of each of the two objects. Sure?
confident?
phone a friend?
should i lock it?
Come on, think over it again. If it is on Ankit's blog it can't be such trivial a thing! If your answer is a, I am going to disprove you in the next couple of minutes.
Actually, it depends on how we define the mass of an object, or, how we define the object itself! Thinking in a trivial way, I would say, the mass of an object is the mass of everything contained within it; irrespective of what the composition is. I'll make it simple now. I'll give you an example where I keep objects of same mass on the two pans of the balance, but the balance would still be inclined on one side.
I have a hollow tennis ball. How do you calculate the total mass of a hollow ball? It is the mass of the shell, plus the mass of the air inside it. Fair enough, right? Now, let's have a similar ball on the other pan. Both balls would weigh the same. The balance will be at equilibrium. Now, let the second ball start shrinking. Let it shrink to half the diameter of the original. Mind it, we've just shrunk the ball, not changed its mass. The ball simply gets denser. The air inside it gets compressed. The overall mass of the ball remains the same. But you will see the balance tilting to the side of this ball, suggesting that this ball is actually becoming heavier. The more you shrink it, the more is the weight as suggested by the balance. So, now we have two balls, of equal mass, on both sides of the balance. And the balance suggests that one of them is heavier. Is it not absolutely strange?
I know you won't take my word for it. So, I will tell you the logical reason behind this. (wow!! when I write sentences like this, it makes me feel like a really educated person, so ignorant and naive though I am ! ). Actually, what acts upon the balance pans apart from the ball's weight is the pressure of air. The atmospheric pressure. Air pressure is nothing but the weight of the air column directly above the pans (consider a cylinder of air with one end on the pan and the other at the end of atmosphere, the weight of air in that cylinder acts on the pan). In the case of the first ball with uncompressed air, what acted upon the pan was the weight of the shell of the ball, plus the air pressure (the weight of the air inside the ball is accounted for, as it is a part of the air column which applies air pressure). In case of the second ball, since we have compressed some air, there is more air in the air column pressing this pan. So, there is a bit more air, plus the shell of the ball, hence the total force on the second pan will be higher. Hence, the balance tilts towards the second pan.
So, you know, things are not that simple. And as I told you had this thing been simple, or uninterestingly complex, it wouldn't be there on my blog!
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1 comments:
interesting observation :)
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