Question
Two balls having different masses reach the same height when shot into the air from the ground.
If there is no air drag, which of the following statements must be true? (More than one statement may be true.)A. Both balls left the ground with the same speed.
B. Both balls left the ground with the same kinetic energy.
C. Both balls will have the same gravitational potential energy at the highest point.
D. The heavier ball must have left the ground with a greater speed than the lighter ball.
E. Both balls have no acceleration at their highest point.
A
A, E
B
B, D
C
Explanation / Answer
Let , masses of the two bodies are M1 and M2 since both the bodies reached the same height when shot into the air from the ground so, by the standered formula , maximum height reahed by the masses are not depend upon their masses (Height=H = u2 / 2 g , where u be the intial velocity of the body ) so, both bodies leaves the ground with same speed Hence , option : A is correct since , kinetic energy of the body = 1/2 Mu2 Here velocities are constanta but masses are different thus, Kinetic energies are not equal , hence B statemet is false As grvitational P.E is mgH However ,heights are equal but masses are different Hence , grvitational P.E at height points are not equal so, statement C is false Heavier ball must have left the ground with a greater speed than the lighter ball, depends upon velocity only but not on mass thus, statemetn D is false At height point both the ball s velocity is 0 , but there acceleration due to gravity acting on them in down word direction Hence , this E statement also will false Thus, among the given option: A is correct At height point both the ball s velocity is 0 , but there acceleration due to gravity acting on them in down word direction Hence , this E statement also will false Thus, among the given option: A is correct