# law of conservation of momentum

A hoop is placed on a absolutely smooth level surface.a beetle alights on the hoop.what trajectory will be described by the beetle and the centre of the loop if the beetle begins to move along the hoop?the radius of the hoop is `R`,its mass is `M` and the mass of the beetle is `m`. nishant bhai please dont answer this.

1
Aneesh Gupta ·

i dont know.. i am guessing .. it is circular?

or elliptical. this i am thinking becasue the hoop will move to one side and then to another.. will come back.. to the same position when the beetle reaches the initial point again!

39
Dr.House ·

its circular.but u have to reason it out.

1
sud ·

why it is circular

33
Abhishek Priyam ·

Is this the question?

1
skygirl ·

one thing... since the center of mass b4 beetle starts moving was zero.... so center of mass will always remain on the same place...

distance of com from center of hoop d= mR/m+M
this distance will always be maintained....

62
Lokesh Verma ·

sky, i think u have given the best possible answer :)

neone who can think of something better?

* I surely cant !

33
Abhishek Priyam ·

Yes.....

Beetle will move in a circle of radius MR/(M+m)

and center of loop in a circle with radius of mR/(M+m)

both around common center (i.e. around initial COM)
Both on opposite side of an imaginary diameter...

39
Dr.House ·

thats really good work priyam bhai and sky

1
skygirl ·

the trajectory will actually be two concentric circles with c.o.m as the center.... center of the loop with radius mR/(m+M) and the beetle wid radius MR/(m+M)....

62
Lokesh Verma ·

elegant :)

1
skygirl ·

ok priyam has posted almost a same ans... but wat about an imaginary diameter... i din get dat....