THREE OBJECTS OF MASSES M1 M2 M3 ARE ALLOWED TO FALL FROM REST AND FROM SAME POINT ALONG THREE FRICTION LESS PATHS.

PROVE THAT ON REACHING GROUND SPEED RATIO WILL BE 1:1:1

Three different object of masses m 1 ,m 2 ,m 3 are allowed to fall from rest from the same point along three different frictionless path, the speed of the three object on reaching the ground will be in ratio of?If the balls falls through the same height, whatever be the frictionless path, their velocity on reaching the ground will be equal. This is according to the law of conservation of energy.If they fall from a point at a height ‘h’ from the ground, the potential energy at the point is, PE = mghThe kinetic energy on reaching the ground is, KE = ½ mv 2Since, PE = KE=> mgh = ½ mv 2=> v = √(2gh)The equation is independent of mass