Question

A boy drops a ball from top of the building such that the mechanical energy possessed by the ball at the topmost point is 50 J. Determine the value of X and Y ignoring the resistance offered by the air during the motion of the ball. (M.E. - Mechanical Energy; P.E. - Potential Energy and K.E. - Kinetic Energy)

• A. X = 30 ; Y = 0
• B. X = 20 ; Y = 0
• C. X = Y = 50
• D. X = 30 ; Y = 50

Answer 1

The correct option is A X = 30 ; Y = 0

A boy drops a ball from top of the building such that the mechanical energy possessed by the ball at the topmost point is 50 J.
According to the law of conservation of mechanical energy, in the absence of air resistance the mechanical energy at every point remains constant, that is 50 J.
The total mechanical energy at every point is the sum of kinetic energy and potential energy.
At the topmost point, potential energy is maximum while the kinetic energy is zero such that,
Potential Energy = Mechanical Energy = 50 J
As the ball starts falling down, its potential energy decreases while the kinetic energy increases.
At a point in between,
Potential Energy = 20 J
Therefore, Kinetic Energy = Mechanical Energy - Potential Energy
X = $50-20$ = 30 J
When the ball reach to a point on the ground, whole of the potential energy gets converted into kinetic energy, such that

Kinetic energy = Mechanical energy = 50 J
Potential energy = Y = 0 J

The correct answer is option C - X = 30; Y = 0.