TIFR 2013 Problem 30 Solution has been written for TIFR entrance series. A problem using the idea of linear independence of vectors from Linear Algebra.
TIFR 2013 Problem 30 Solution has been written for TIFR entrance series. A problem using the idea of linear independence of vectors from Linear Algebra.
TIFR 2013 Problem 29 Solution has been written for TIFR entrance preparation series. A problem on sequence criterion for continuity from Real analysis.
Let's find out the centre of mass for carbon monoxide, useful for the Olympiad. Try it yourself before reading the solution.
Let's discuss an interesting problem - Loop-The-Loop, useful for Physics Olympiad. Try it yourself before reading the solution.
Let's discuss a problem where we will find out the total charge on a circular disc. The Problem: Consider a circular disc of radius (a) whose surface density of charge at any point ((r,\theta)) is $$ \sigma(r,\theta)=\sigma_0r^2sin^2\theta$$ Find the total charge on the disc. Solution: Consider a surface element (rdrd\theta) on the disc about the […]
TIFR 2013 Problem 28 Solution written for TIFR entrance preparation series. A problem on inverse of a continuous map from real analysis
Let's discuss the problem where we have to find the potential of metal sphere. The Problem: A metal sphere having a radius (r_1) charged to a potential (\phi_1) is enveloped by a thin-walled conducting spherical shell of radius (r_2). Determine the potential (\phi_2) acquired by the sphere after it has been connected for a short […]
A heavy load is suspended on a light spring with upper half rigidity (2k). The spring is slowly pulled down at the midpoint (a certain work (A) is done thereby) and then released. Determine the maximum kinetic energy (W_k) of the load in subsequent motion. Solution: If the middle of the spring is stretched out […]
TIFR 2013 Problem 27 Solution written for TIFR entrance preparation series. A problem on Bounded derivative and compactness from real analysis
The cosmonauts who landed at the pole found that the force of gravity there is (0.01) of that on the Earth, while the duration of the day on the planet is the same as that on Earth. It turned out that besides that the force of gravity on the equator is zero. Find the radius […]