JEE Advanced 2020 Concept Recapitulation Test 4 Paper 2

As the plank retards 1kg block will move relative to the plank but 2kg block will remain at rest distance travelled by 1kg block in 1sec.
Sr=‌

1

2

×ar×t2=‌

1

2

m
Relative velocity of 1kg after 1secVr=1m∕s
Then using conservation of linear momentum and Newtons experimental Law V1+2V2=1−−−−(1)
V1−V2=−‌

1

2

−−−−(2)
⇒V1=0&V2=‌

1

2

m∕s
Final separation between blocks =‌

(1∕2)2

2×2

=‌

1

16

m