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 […]
Let's discuss a beautiful problem from Physics Olympiad based on Velocity and Acceleration. The Problem: Velocity and Acceleration A particle is moving in positive x-direction with its velocity varying as v= α√x. Assume that at t=0, the particle was located at x=0. Determine the the time dependence of velocity acceleration the mean velocity of the […]
Understanding the Infinitesimal Cheenta Notes in Mathematics Let's discuss a beautiful idea related to progress in mathematics and understanding the infinitesimal. Adding infinitely many positive quantities, you may end up having something finite. Greeks did not understand this very well. Archimedes had some ideas. Kerala school of mathematics under the leadership of Madhavacharya made […]
The distance travelled by an object is given by x=(at+bt2)/(c+a) where t is time and a,b,c are constants. The dimension of b and c respectively are: [L2T-3], [LT-1] [LT-2], [LT-1] [LT-1], [L2T1] [LT-1], [LT2] Solution: The dimension of x is L. Hence, the dimension of a must be LT-1. Dimension of c and a are […]
Try this problem useful for the Physics Olympiad based on Motion of an Elevator. The Problem: Motion of an Elevator An elevator of mass M is accelerated upwards by applying a force F. A mass m initially situated at a height of 1m above the floor of the elevator is falling freely. It will […]
Try this problem from ISI B.Stat, B.Math Subjective Entrance Exam, 2017 Problem no. 3 based on Differentiability at origin. Problem: Differentiability at origin Suppose \( f : \mathbb{R} \to \mathbb{R} \) is a function given by $$f(x) = \left\{\def\arraystretch{1.2}%\begin{array}{@{}c@{\quad}l@{}}1 & \text{if x=1}\\ e^{(x^{10} -1)} + (x-1)^2 \sin \left (\frac {1}{x-1} \right ) & \text{if} x […]
Let's discuss a beautiful problem useful for Physics Olympiad based on Impulse and Momentum. The Problem: A particle of mass m is made to move with uniform speed v along the perimeter of a regular hexagon. Magnitude of impulse applied at each corner of the hexagon is (a) mv (b) mv√3 (b) mv/2 (d) zero […]