Answer :
The number of collisions is 26. An elastic collision is one in which the system does not experience a net loss of kinetic energy as a result of the collision.
Two objects collide in an elastic collision when no kinetic energy is wasted. The kinetic energy and momentum of the objects are conserved when they bounce back from one another. We are dealing with an elastic collision because inelastic collisions are thought to happen when the two items stay together after the collision.
Initial energy equals E o
=2MeV=2×10 6 \s eV
After the initial collision, E 1 = 2 E o
After a second collision, E 2 equals 2 E 1.
\s = \s2 \s2
E \so \s
When there is a third collision, E 3 equals 2 E 2.
\s = \s2 \s3
E \so \s
And so
Following n collisions, E n = 2 n
E \so \s
final energy = 0.04 eV
Consequently, E n = 0.04
⟹ \s2 \sn
2×10 \s6
\s =0.04
⟹2 \sn \s = \s0.04 \s2×10 \s6
\s =5×10 \s7
n=log 2 (510 7 )=log 10 2 log 10 (510 7 )
⟹n= \s0.301 \s7+0.699
⟹n=26
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