Inequalities Involving A.M, G.M, H.M Let A, G and H be Arithmetic, Geometric, and Harmonic means of two positive numbers a and b. Then, , and . These three means possess the following property. A ≥ G ≥ H. Proof: We have , and . , , , , A ≥ G … (1) , Read more about Inequalities Involving A.M, G.M, H.M[…]
Heat Engine Efficiency A heat engine is a device that converts heat into work continuously through a cyclic process. It takes heat from a reservoir then does some like moving a piston, lifting weight etc. and finally discharging some of the heat energy into the sink. Schematically it can be represented as: The essential parts Read more about Heat Engine Efficiency[…]
Magnetic Maps and Neutral Points Magnetic Maps: Magnetic map is obtained by drawing lines on the surface of earth, which passes through different places having same magnetic elements. Magnetic maps i.e.., declination, dip and horizontal component over the earth vary in magnitude from place to place. It is found that many places have the same Read more about Magnetic Maps and Neutral Points[…]
Diameter from of the Equation of a Sphere Let AB be the diameter of a sphere whose centre is C. let the vectors of the extremities A and B of the diameter be and , respectively. Let P be any point on the spheres. Suppose the position vector of P is . We know that Read more about Diameter from of the Equation of a Sphere[…]
Resultant Amplitude and Intensity Intensity if the power transferred per unit area that is perpendicular to the direction of propagation of the energy. Intensity is directly proportional to square root of the amplitude. So, if intensity becomes double, then amplitude will become four times. Let us consider two waves that have the same frequency but Read more about Resultant Amplitude and Intensity[…]
Regular Tetrahedron A regular tetrahedron is one in which all four faces are equilateral triangles. Angle between any Edge and Face not Containing that Edge of Regular Tetrahedron: Let us find the angle between edge OA and face OBC. Since tetrahedron is regular and its face is an equilateral triangle, the required angle is the Read more about Regular Tetrahedron[…]
Thermal Capacity Thermal Capacity of a substance is defined as the amount of heat required to change its temperature through one degree. If Q is the amount of required to change the temperature of a body of mass m through, then Q = msΔθ If temperature difference = 1, then Q = ms The value Read more about Thermal Capacity[…]
Image of a Point in a Plane Distance of a point From a Plane – Cartesian Form: Let PM be the length of the perpendicular from a point P (x₁, y₁, z₁) to the plane ax + by + cz + d = 0. Then the equation of PM is . The coordinates of any Read more about Image of a Point in a Plane[…]
Distance of a Point from a Plane – Vector Form Vector Form: Let be the given plane and be the given point. Let PM be the length of the perpendicular from P to the Plane π. Since line P passes through and is parallel to vector , which is normal to the Plane π, the Read more about Distance of a Point from a Plane – Vector Form[…]
Collision between Bullet and Vertically suspended block A collision is said to have taken place if two bodies interact with each other and undergo a change in momentum and or kinetic energy. A bullet of mass m is fired horizontally with velocity u in block of mass M suspended by vertical thread. After the collision Read more about Collision between Bullet and Vertically suspended block[…]