This question has statement -I and statement - II of the four choices given after the statements , choose the one that best describes the two statements .
Statement - I : A point particle of mass m moving with speed v collides with stationary point particle of mass M . If the maximum energy loss possible is given as `f(1/2 mv^(2)) " then" F = (m/(M+m))`
Statement -II : Maximum energy loss occurs when the particles get stuck together as a result of the collision .

Options

A. Statement - I is true , Statement - II is true Statement - II is a correct explanation of Statement -I
B. Statement -I is true , Statement -II is true Statement -II is not a correct explanation of Statement -I
C. Statement -I is true , Statement -II is false .
D. Statement -I is false , Statement -II is true .

Answer

D

Explanation

Kinetic energy before collision - Kinetic energy after collision = energy loses
`1/2 mv^(2)+1/2 M(o)^(2)-1/2 (m+M)(v)^(2)`
= energy loses
Where `v = (mv+M xxo)/(m+M)`
` :. V. =m/(m+M) v`
`1/2 mv^(2)-1/2 (m+m)(m/(m+m)v)^(2)=` Energy loses
` :. 1/2 mv^(2)-1/2 mv^(2)xx(m/(m+m)v)^(2)` = Energy loses
` :. 1/2 mv^(2)[1-m/(m+m)]^(2)` = Energy loses
` :. 1/2 mv^(2)[1-m/(m+m)]^(2)` = Energy loses
`:. f = M/(m+M)`
here in statement - I `m/(m+M)` is given .
` :. ` Statement -I is wrong and energy loses becomes positive so maximum energy will be dissipated and hence statement -II is correct .