Question

A block of mass M is attached to a horizontal spring and is executing SHM, with amplitude A1. When the mass M passes through its mean position, a smaller mass m is placed over it gently and both of them move together with amplitude A2. The ratio of (A1A2) is

- M+mM
- √M+mM
- MM+m
- √MM+m

Solution

The correct option is **B** √M+mM

Mean position is the equilibrium point.

i.e Fnet=0

So, linear momentum is conserved.

Pi=Pf⇒MV1=(M+m)V2

where, V1= velocity of block M at mean position.

V2= velocity of combination of blocks at mean position.

We know,

V1=A1ω1:V2=A2ω2

where ω1=√KM, ω2=√KM+m

⇒MA1w1=(M+m)A2w2

⇒MA1√KM=(M+m)A2√KM+m

∴A1A2=(√KM+m)(M+m)√KM×M=√M+mM

Mean position is the equilibrium point.

i.e Fnet=0

So, linear momentum is conserved.

Pi=Pf⇒MV1=(M+m)V2

where, V1= velocity of block M at mean position.

V2= velocity of combination of blocks at mean position.

We know,

V1=A1ω1:V2=A2ω2

where ω1=√KM, ω2=√KM+m

⇒MA1w1=(M+m)A2w2

⇒MA1√KM=(M+m)A2√KM+m

∴A1A2=(√KM+m)(M+m)√KM×M=√M+mM

Suggest corrections

0 Upvotes

Similar questions

View More...

People also searched for

View More...

- About Us
- Contact Us
- Investors
- Careers
- BYJU'S in Media
- Students Stories - The Learning Tree
- Faces of BYJU'S – Life at BYJU'S
- Social Initiative - Education for All
- BYJU'S APP
- FAQ
- Support

© 2021, BYJU'S. All rights reserved.