JEE Advanced 2017 Paper 1

Net external force acting on the system along the x-axis is zero.
∴Along the x-axis
Momentum is conserved
⇒mv=MV
From conservation of energy
Loss in GPE of particle of mass m = Gain in kinetic energy of both the masses
⇒mgh=

1

2

mv2+

1

2

MV2⇒mgh =

1

2

mv2+

1

2

M(

mv

M

)2
⇒2gh=(1+

m

M

)v2⇒v =√

2gh

1+ m M

hence option (A) is correct.
Hence option [B] is incorrect.
Since the location of center of mass does not change along the x-axis
mΔx

m

G

+MΔx

M

G

=0 ⇒m(R−x)−Mx=0f
x=

mR

m+M

.
Δx

M

G

=

−mR

m+R

Hence option (D) is correct
Δx

m

G

=R−x=

MR

M+m

Final position of m=−x−

mR

M+m

Hence option (C) is incorrect.