$\pi$ and e (the base of the natural logarithm) are two of the most important and widely studied mathematical constants. Although they seem very different from each other, they are actually closely related through various mathematical formulas. Continue reading Relationship Between $\pi$ and e
Laws of Motion ~ Quote
“The laws of motion dictate that a pebble thrown upwards and a planet orbiting a star are both governed by the same principles, reminding us that the universe is interconnected and bound by a set of fundamental rules.”
Flying Bird ~ Q & A
Q: A bird while flying takes a right turn, where does it get the centripetal force from?
A: The centripetal force is provided by the bird’s wings as it changes the direction of its flight. As the bird turns to the right, it must adjust the angle of its wings to produce a component of the force towards the center of the turn.
Potential Energy of Book ~ Q & A
Q: One person says that the potential energy of a particular book kept in a bookshelf is 25 J and the other says it is 35 J. Is one of them necessarily wrong?
A: It is possible that one of them is wrong, but it is also possible that both are correct.
The potential energy of an object depends on its position and the reference point chosen to calculate it. If both individuals are using different reference points to calculate the potential energy of the book, then they may obtain different values. Continue reading Potential Energy of Book ~ Q & A
Sound Pitch ~ Q & A
Q: If two people talk in a room having Helium gas higher than usual, will they hear any change in the pitch of sound? Continue reading Sound Pitch ~ Q & A
For a triangle, show that the point where altitude …
For a triangle, show that the point where altitude cuts circumcircle is the image of the orthocentre about the side.
Solution
Let ABC be triangle having H as orthocentre. The proof is given below for reflection about side BC. Similar approach can be used for reflections about other sides. Continue reading For a triangle, show that the point where altitude …
Wave Pulses ~ Q & A
Q: Two wave pulses identical in shape but inverted with respect to each other are produced at the two ends of a stretched string and are moving in opposite directions with same speed. At an instant when the pulses reach the middle of the string, the string becomes completely straight. What happens to the energy of the two pulses at this instant? Continue reading Wave Pulses ~ Q & A