A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

Options

A. 0.68
B. 0.41
C. 2
D. 1

Answer

B

Explanation

When a stone is dropped from a height h , it hits the ground with a momentum
`P= m sqrt(2gh)`
when m is the mass of the stone
when the same stone is dropped from a height `2h` ( i.e, 100 % of initial ) then its momentum with which it hits the ground becomes
` P. =m sqrt(2 g (2h)) = sqrt(2)P` ( using (i))
% change in momentum `= (p.-P) /(p ) xx 100 % `
` =( sqrt(2)P-P )/( P ) xx 100 % = 41 %`