IIT JEE , AIEEE Forum - Physics , Mechanics - this is from ROTATIONAL MOTION,MOMENT OF INERTIA(2ND ONE)

rakhiagrawal

1.IN A BICYCLE RADIUS OF REAR WHEEL IS TWICE THE RADIUS OF FRONT WHEEL.IF Rf &Rr are THE RADIUS OF,Vf &Vr ARE SPEEDS OF TOPMOST POINTS OF WHEEL THEN

(A)Vr=2Vf

(b)Vf=2Vr

(C)Vf=Vr

(d)Vf>Vr

explain how?

pannaguma

let Vcm be velocity of bicycle.
for each wheel draw a triangle, with vertical line passing thre top centre and bottom. now draw lines indicating magnitudes of velocities. Vtop = Vcm*radius for both cases.

thus Vrear = 2 Vfront.

rakhiagrawal

sorry my friend.i couldn't create the diagram in my mind according to ur explanation & the ans. given is that both are equal.

rakhiagrawal

plz.any 1 give some idea.

rooney

EDIT : I gave a shitty answer here

karthik2007

I am getting option c)

Now, as the cycle as a whole moves with the same speed, the speeds of the centers, ie, the center of mass of the two wheels will be the same, and let it be V.

Consider the rear wheel:

(I hate super and subscripts!! )

Let the speed of the center of mass be V

Let the radius of the rear wheel be R'', and radius of the front wheel be R', and the corresponding notations be used for the velocities of the topmost points.

Now, as the bottommost point is the point of zero velocity (instantaneous)

We have w = V/2R'.

So, v' = 0 + 4R'(V/2R') = 2V.
(As V of bottommost point = 0) - thanks for pointing it out rooney :) )
For the rear wheel :

w = V/R'.

so, v'' (topmost point) = 2R(V/R) = 2V.

So, net speed of the topmost point = 0+2V = 2V

Hence, its clear that both the points move with same velocity of 2V_com .

karthik2007

rakhia, you there?

rooney

Karthik, you are right.

Answer is C.

But w is not same for both the wheels.

rakhiagrawal

yas,w is not same for both.but w & r changes such that v remains constant.but i didn't get how the values of v' & v" came in kartic's ans.

rooney

It is calculated by Velocity at point B = Vector sum of ( Velocity at point A + w x Distance of B from A)

rakhiagrawal

i m really sorry.but can u plz........... give me the diagram indicating those points in any one case.

karthik2007

Here it is -

Hope it helps you out.

rakhiagrawal

yes,any one.but plz. indicate point A & B as given by rooney so that i can apply the formula given.tankks a lot in advance.

rakhiagrawal

finally i understood this & i am satisfied bcoz of u karthik.i don't have words to thank u. thank u verymuch.

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