answer: (B) 41%
Explanation
A stone is dropped from a height of h in the first scenario. We may deduce from the equations of motion that the velocity of the stone in free fall is given by:
v = √2gh——(1)
where
- g is the acceleration due to gravity
- h is the height from which the stone is dropped.
Also, the momentum of the stone is given by
p=mv——(2)
where
- p is the momentum of the stone
- m is the mass of the stone
- v is the velocity of the stone
Let this be equation 2. Substituting equation 2 in equation 1, we have
p = mv = m√2gh−−−(3)
Now, let us move on to the second case.
Here, the stone is dropped from a height 100% more than the previous height.
If we call this height H, it is given by
H = h + 100/100h = 2h
Again, if we take the velocity of this stone to be V, it is given by
V=√2gH =√2g(2h) 2√gh−−–(4)
Similarly, if the momentum of the stone in the second case is P, it is given by
P = mV = m2√gh−−–(5)
Now, to calculate the change in momentum, we subtract equation 3 from equation 5, as follows
P−p=mV−mv=m2√gh – m√gh = m√gh (√2-1) = 0.41m√gh
finally, to get the change in momentum in percentage, we take the ratio of this change in momentum to the original momentum and multiply by 100%.
This is shown as follows.
P−p/p x 100% 0.41m√gh/ m√gh x 100% =41%