A particle of mass $$1$$ kg has velocity $$v1=(2t)$$ $$i^$$ and another particle of mass $$2$$ kg has velocity $$v2=(t2)$$ $$j^$$. Match the following columns and mark the correct option from the codes given below.CodesA B C

Question

A particle of mass $$1$$ kg has velocity $$v1=(2t)$$ $$i^$$ and another particle of mass $$2$$ kg has velocity $$v2=(t2)$$ $$j^$$. Match the following columns and mark the correct option from the codes given below.CodesA  B  C

Infinity Learn · Accepted Answer

$$FCM=F1+F2=m1a1+m2a2=(2i^+8j^)$$∴         $$FCM=4+64$$⇒$$FCM=68unit$$                 $$vCM=m1v1+m2v2m1+m2=(1)(4i^)+(2)(4j^)3=4i^+8j^3$$∴           $$vCM=1316+64=803unit$$                       $$s1=$$∫$$02v1dt=(4i^)$$                       $$s2=$$∫$$02v2dt=83j^Now$$,        $$sCM=m1s1+m2s2m1+m2=(1)(4i^)+283j^3=43i^+169j^$$∴        $$sCM=169+25681=209unitHence$$, A→q, B→r, C→p.

Column I	Column II
(A) Net force on centre of mass at 2 s	(p) $\frac{20}{9}$ unit
(B) Velocity of centre of mass at 2 s	(q) $\sqrt{68} unit$
(C) Displacement of centre of mass in 2s	(r) $\sqrt{80} / 3 unit$
	(s) None

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material