Recent content by Miraj Kayastha

Since lnx is defined for positive x only shouldn't the derivative of lnx be 1/x, where x is positive. My books does not specify that x must be positive, so is lnx differentiable for all x?

I think its "φ/ω" http://www.intmath.com/trigonometric-graphs/3-graphs-sin-cos-phase-shift.php

There are two waves y1=a. sin(ω.t) & y2=a. sin(ω.t + φ) My question is what is the phase difference of these two waves? Is it "φ" or "φ/ω"?

I did not get my answer from that. I need the derivation

I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from...

Why did you put the magnitude of force, shouldn't it contain minus sign as well? Because F is in opposite direction to r? I read a post online that said if we state -dr we are already assuming the motion of the body is downwards so the limits should be switched and if we state dr then only we...

I am still not clear about the integration because the work done by a variable force is ∫F.dx where dx is a very small DISPLACEMENT. Whereas while calculating the work done by the gravitational force we do ∫F.dr where dr is a radial displacement that is always outwards. So is dr equal to dx? I...

If dr is negative in case of a falling object, the integration gives a negative result since the lower limit will be greater than the upper limit. So, what's wrong?

"dr" is used when potential energy is derived from integration. Here is dr a small displacement in the direction of r? To calculate the work done by gravity using integration when a body if falling is dr positive or negative?

What does the "r" in the formula F = - GMm/r^2 mean? Does it mean distance between the two bodies or the radial displacement ? Is the "r" a vector or a scalar?

Here when you said "when we push it back with the same magnitude, you do F x D work again" I think we should also account the direction of the force because the force is constant both in magnitude and direction throughout the motion. So shouldn't the work done by the force on the crate when...

Yes I have.

In a closed loop when we apply an applied force on an object the object starts at point A and stops at point A. Since the displacement is 0, Work done by the applied force on the object is = F x s x cosθ...

is GPE at a point the work we must do against the gravitational force to bring an object from infinity to the point? Or is it the work done by the gravitational force?

Here you said the system gains energy because Earth also does negative work on the mass.