A pen of mass 'm' is lying on a piece of paper of mass M placed on a rough table. If the cofficient of friction between the pen and paper and, the paper and the table are (\mu_1) and (\mu_2) respectively, what is the minimum horizontal force with which the paper has to be pulled […]
Notes in Mathematics A Cheenta Newsletter I hope you are doing well. First, let me congratulate all students from India and abroad who did exceptionally well in contests like I.S.I. and C.M.I. Entrance, Math Olympiads, and other science olympiads. Among our students, Aniruddha, Sambudda, and Mary deserve a special mention. Today I wish […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Particle Motion. The Problem: Particle Motion A particle Q is moving +Y axis. Another particle P is moving in XY plane along a straight line x=-d (d>0) with a uniform speed v parallel to that of Q. At time t=0, particles P and Q […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Angle between Force and Momentum. The Problem: Angle between Force and Momentum A particle moves in the X-Y plane under the influence of a force such that its linear momentum p(t)=A[icos(kt)-jsin(kt)] where A and k are constants. Find the angle between the force and […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Motion in an Electric Field. The Problem: Motion in an Electric Field A particle moves rectilinearly in an electric field E=E0-ax where a is a positive constant and x is the distance from the point where the particle is initially at rest. Let the […]
Try this beautiful problem from TIFR 2013 problem 3 based on the roots of an equation. Problem: TIFR 2013 problem 3 The equation \(x^3+3x-4=0\) has exactly one real root. Discussion Hint: Try differentiating. Is the function monotonic? Note that the cubic equation has at least one real root (fundamental theorem of algebra provides for three […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Power and Acceleration. The Problem: Power and Acceleration Assume that a constant power P is supplied to an electric train and it is fully used in accelerating the train. Obtain relation giving the velocity of the train and distance traveled by it as functions […]
Let's discuss a problem useful for Physics Olympiad based on Instantaneous Acceleration. The Problem: Velocity-displacement curve of a particle moving in a straight line is as shown 2m/s2 5 m/s2 1 m/s2 Zero Discussion: Acceleration a=v dv/ds From, the graph, we can see a=vtanθ tanθ=1/4 Putting the values, we get acceleration a= 1m/s2
Let's discuss a problem useful for Physics Olympiad, based on Projectile Inside a Liquid. The Problem: Projectile Inside a Liquid A body of mass m is projected inside a liquid at an angle θ0 with the horizontal at an initial velocity v0. If the liquid develops a velocity-dependent force F= -kv where k is a […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Motion under Constant Gravity. The Problem: Motion under Constant Gravity A person throws vertically up n balls per second with the same velocity. He throws a ball whenever the previous one is at its highest point. The height to which the balls rise is […]