Question

STATEMENT-1 - A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the max energy loss possible is given as f(mv^{​​​​​2}/2), then f=(m/M+m).

STATEMENT-2 - Max energy loss occurs when the particles get stuck together as a result of the collision.

A) Both S1 and S2 are true, S2 explains S1 correctly

B) Both S1 and S2 are true, S2 does not explain S1

C) S2 is false, S1 is true

D) S1 is false, S2 is true

Explain in detail.

Answer 1

Statement 2 is true.It is provable that in such collision energy loss is maximum when one particle get stuck with another.I think this could be proved in your curicculum or if you want it proved you can ask this as next question i will prove it for you.
so moving to the second statement
as from statement 2 maximum energy loss is when the bodys stuck together
so
From law of conservation of momentum
mv+M*0= (m + M) v′
v'=m/(M+m)v
From here on wards i wil use term 'square in equations due to limitations of my keypad please pardon me.
loss in kE=KEinitial-KEfinal
KEinitial=1/2 m(v square)
KEfinal=1/2 (M+m)(v' square)
=1/2(M+m)(((m/M+m)*v ) Allsquare)
=1/2 (M+m)((m/M+m)square)(v square)
=
1/2 (m square)/(M+m)*(v square)
KEloss=1/2 m(v square)-1/2((m square/M+m)v square)
1/2 m(v square)(1-m/(M+m))
1/2 m(v square)(M/(M+m)
F(m(v square)/2)
F=M/(M+m)
not m/(M+m)
Hence statement 1 is false but 2 is true