TIFR 2014 Problem 4 Solution has been written for TIFR entrance preparation series. A problem on uniform continuity from mathematical analysis.
TIFR 2014 Problem 4 Solution has been written for TIFR entrance preparation series. A problem on uniform continuity from mathematical analysis.
Let's solve the problem based on Magnetic Field at Focus of Parabola and learn how to solve it. First, try it yourself, then check your solution. The Problem: An infinite wire carrying current (I) is bent in the form of a parabola. Find the magnetic field at the focus of the parabola. Take the distance […]
Let's discuss a problem where we will find the change in the orbit of the planet. Give it a try first, then read the solution.
TIFR 2014 Problem 3 Solution has been written for TIFR entrance preparation series. A problem on bounded function from mathematical analysis.
TIFR 2014 Problem 2 Solution has been written for TIFR entrance preparation series. A problem on continuous bounded function from Real analysis.
TIFR 2014 Problem 1 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects. The image is a front […]
An ice skater spins at (4\pi )rad/s with her arms extended. If her moment of inertia with arms folded is (80\%) of that with her arms extended, what is her angular velocity when she folded her arms? Discussion: Conservation of angular momentum gives $$ I_1\omega_1=I_2 \omega_2$$ $$ (I_1) (4\pi)=0.8 I_1 \omega_2 $$ Hence, (\omega_2=5\pi)
Let's discuss a problem on angular momentum and prove that the tension in the thread is inversely proportional to the cube of the distance from the hole. The Problem: A small mass m tied to a piece of thread moves over a smooth horizontal plane/ The other end of the thread is drawn through a […]
TIFR 2013 Problem 40 Solution has been written for TIFR entrance preparation series. A problem on alternatig series from mathematical analysis.
A ring of radius (r) is located in the (x-y) plane is given a total charge (Q=2\pi R\lambda). Show that (E) is maximum when the distance (z=r/\sqrt{2}). Discussion: The elctric field at distance z from the centre of the ring on the axis of the ring with charge (Q=2\pi R\lambda) is given by $$ E=\frac{\lambda […]