the answer is the third option, mechanical enrgy is conserved.
To be eligible to answer this question, you should know what Law of Conservation of Mechanical Energy is. It states that, "The total mechanical energy of the system is conserved at all times iff there is no resultant external force acting on it". Only if you assume that there is no air resistance.
Hence, the bowling ball conserved mechanical energy.
You can even derive it if you want to understand more deeply.
Consider the ball at two instances, A and B
At A, i.e the ball is 2.5 metres off the ground when it falls. So,
Mass(m)= 2kg , Height(h) = 2.5 m , Acceleration due to gravity(g) = 9.8m/s*2 , Velocity(v)= 0m/s
because it falls at that instance
Now,
Totale Mechanical Energy= P.E + K.E
at that instance
where P.E is Potential Energy and K.E is Kinetic Enerygy
T.E = mgh + 1/2mv*2
T.E = (2)(2.5)(9.8) + 0
T.E = 49J .....................(1)
At B, i.e just before the ball reaches the ground and is travelling at a speed, 7m/s
So,
m= 2kg , h= 0 (because it is negligible) , g=9.8m/s*2 ,
v= 7m/s
Now, w.k.t
T.E = P.E + K.E
T.E = 0 + (1/2)(2)(7)(7)
T.E = 49J ....................(2)
From eq.s (1) and (2) we conclude that mechanical energy is conserved at all times iff there is no resultant external force acting on the body and by neglecting air resistance.
I hope I was helful :)