Let's discuss a problem useful for Physics Olympiad based on Dimensional Analysis. The Problem: Dimensional Analysis Consider an expression F=Ax(sin^{-1} (Bt)) where F represents force, x represents distance and t represents time. Dimensionally the quantity AB represents (A) energy (B) surface tension (C) intensity of light (D) pressure Solution: The quantity Ax on RHS must […]
TIFR 2013 Problem 8 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 […]
Try this problem from TIFR 2013 problem 4 based on Lower bound of roots. Question: TIFR 2013 problem 4 True/False: The equation \(x^3 + 10x^2 − 100x + 1729 = 0\) has at least one complex root α such that |α| > 12. Hint: What happens if \(|\alpha| \le 12\) for all roots \(\alpha?\) Discussion: Let […]
Let's discuss a beautiful Problem, useful for Physics Olympiad based on Force on a Wooden Cube. The Problem: Force on a Wooden Cube A wooden cube is placed on a rough horizontal table. A force is applied to the cube. Gradually the force is increased. Whether the cube slides before toppling or topples before sliding […]
TIFR 2013 Problem 6 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 […]
Let's discuss this beautiful Cattle and Hay Problem useful for Physics Olympiad. The Problem: The Cattle and Hay Problem An airplane is dropping bales of hay to cattle. The pilot releases the bales at 150m above the level ground when the plane if flying at 75m/s in a direction above \(55^\circ\) above the horizontal. How […]
Let's discuss the beautiful snowball problem useful for Physics Olympiad. The Snowball Problem: (a) A snowball rolls off a barn roof that slopes downward at an angle of \(40^\circ\). The edge of the roof is 14.0m above the ground and the snowball has a speed of 7.00m/s as it rolls off the roof. How far […]
Let's discuss a beautiful problem useful for Physics Olympiad based on the Conical Pendulum. The Conical Pendulum Problem: An inventor designs a pendulum clock using a bob with mass m at the end of a thin wire of length L. Instead of swinging back and forth, the bob is to move in a horizontal circle […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Vector Analysis. Vector Analysis Problem: Let (\vec{a}=6\vec{i}-3\vec{j}-6\vec{k}) and (\vec{d}=\vec{i}+\vec{j}+\vec{k}). Suppose that (\vec{a}=\vec{b}+\vec{c}) where (\vec{b}) is parallel to (\vec{d}) and (\vec{c}) is perpendicular to (\vec{d}). Then (\vec{c}) is (A)(5\vec{i}-4\vec{j}-\vec{k}) (B) ( 7\vec{i}-2\vec{j}-5\vec{k}) (C) (4\vec{i}-5\vec{j}+\vec{k}) (D) (3\vec{i}+6\vec{j}-9\vec{k}) Discussion: In the given problem, (\vec{a})=(6\vec{i}-3\vec{j}-6\vec{k}) $$\vec{d}=\vec{i}+\vec{j}+\vec{k}$$ and $$\vec{a}=\vec{b}+\vec{c}...(i)$$ […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Suitcase Falling from an Airplane. The Problem: Suitcase Falling from an Airplane An airplane is flying with a velocity of \(90m/s\) at an angle of \(23^\circ\) above the horizontal. When the plane is \(114m\) directly above a dog that is standing on level ground, […]