Two cars of masses m1 and m2 are moving in a circle of radii r1 and r2 , respectively. Their speeds are such that they make complete circles in the same time t.The ratio of their centripetal acceleration?

Question

Two cars of masses m1 and m2 are moving in a circle  of radii r1 and r2 , respectively. Their speeds are such that they make complete circles in the same time t.The ratio of their centripetal acceleration?

anonymous · Answer

@ajprincess

shubhamsrg · Answer

is the ans p1/p2 ? where p=momentum ?

anonymous · Answer

ac = v^2/r

anonymous · Answer

no  the answer is  m1 r1 : m2 r2

anonymous · Answer

i wonder hw that mass came there

anonymous · Answer

becoz centripetal force = mv^2/r.......but the question asks for centripetal acceleration

shubhamsrg · Answer

shouldnt ans be m1v1 / m2v2 ?

shubhamsrg · Answer

instead of r1 ?

shubhamsrg · Answer

and r2 *

anonymous · Answer

i am confused

shubhamsrg · Answer

see a1 = m1(v1)^2  / r1
and a2 = m2(v2)^2  /r2
you have to find a1/a2 = (m1v1 / m2v2) * ( v1r2 / v2r1)

now t = 2pi r1/v1 = 2pi r2/v2 
=>v1r2 = r1v2
so req ratio = m1v1 / m2v2

anonymous · Answer

first of all  @shubhamsrg   centripetal acceleration = v^2/r

shubhamsrg · Answer

ohh yes..sorry..

shubhamsrg · Answer

really sorry..

shubhamsrg · Answer

well v1 and v2 are not mentioned in the ques..and ans comes out to be v1/v2
we need to fine a relation between m,v and r now..hmm..

shubhamsrg · Answer

i dont see mass coming from any where..
since v1/v2 = r1/r2
i'd say thats the ans..

anonymous · Answer

Accelerations are independent of mass.It might be given to confuse you.
Anyway,Since the cars take the same time to go around the circle, angular velocity = 2*pi/t = same for both cars.

Let the centripetal accelerations be a1 and a2.v= r *angular velocity.

a1 = v1^2/r1 = r1*(angular velocity)^2,

a2 = v2^2/r2 = r2*(angular velocity)^2 

a1/a2 = r1/r2 .

anonymous · Answer

@kartiksriramk  but in the book it is given as  m1 r1 : m2 r2

anonymous · Answer

Please check it again.I am pretty sure that the ratio is r1/r2.

anonymous · Answer

i also got that...... the options ar  r1 : r2   ,   m1r1:m2r2

anonymous · Answer

Then it is definitely  r1 : r2 .

anonymous · Answer

but the answer is given as  m1r1:m2r2

anonymous · Answer

It must be wrong.

anonymous · Answer

i dont think

anonymous · Answer

i will show the proof

anonymous · Answer

Okay.

anonymous · Answer

attachment

anonymous · Answer

AIEEE question

anonymous · Answer

and this is a model answer paper

anonymous · Answer

Did you check the answer key?

anonymous · Answer

he may be wrong @kartiksriramk

experimentx · Answer

they have same angular velocity,|dw:1345129570006:dw|
hence the required result follows