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, […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Mass supported by a Hollow Cylinder. The Problem: A mass m is supported by a massless string wound on a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass […]
A boy is standing on top of a tower of height 85m and throws a ball in the vertically upward direction with a certain speed. If 5.25 secs later he hears the ball hitting the ground, then the speed with which the boy threw the ball is ( take g=910m/s2, speed of sound in air=340m/s) […]
Let's discuss a beautiful problem useful for Physics Olympiad based on masses over a frictionless pulley. The Problem: Masses over a frictionless pulley Two bodies A and B hanging in the air are tied to the ends of a string which passes over a frictionless pulley. The masses of the string and the pulley are […]
A soldier carrying a gun with parachute A soldier with a machine gun, falling from an airplane gets detached from his parachute. He is able to resist the downward acceleration if he shoots 40 bullets a second at the speed of 500m/s. If the weight of a bullet is 49gm, what is the weight of […]