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A homogeneous sphere $S,$ a uniform cylinder $C,$…

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Problem 95 Easy Difficulty

A homogeneous sphere $S,$ a uniform cylinder $C,$ and a thin pipe $P$ are in contact when they are released from rest on the incline shown. Knowing that all three objects roll without slipping, determine, after $4 \mathrm{s}$ of motion, the distance between $(a)$ the pipe and the cylinder
(b) the cylinder and the sphere.

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Video Transcript

Hello, friends. Here it is. Given a spear. Uniforms, surrender and fight are in contact when they're released from rest the initial velocities Europe on the inclined souls. It is given all the three rules without helping. So there is a your ruling mission off each. How? After four seconds, we have to calculate, but it distance between five and surrender and second part distance between surrender and the spirit. Let us start solving it. We will draw the free body diagram off the body. This is the only plentifully on with. This is the body may be surrendered. Maybe by so here, normal reaction will act. This is the direction along with the weight will act. This is the radius art on. This is better with it having marched into acceleration in this direction and I into ALPA. And on this direction, this will be the instantaneous center. See, in general, moment of inertia, correct top marks into his square off radius operation and acceleration will be our into a helper celebrating the moment off about three point taking clockwise to be positive. Wait. And to sign off Peter in tow. Art. It's called to I l for less and a are Wait is empty. Sign off, Peter in tow. Earth Moment often will say about Cem Center off Months and Kate Square help. And here is I'll find towards So from here you will get Al for two weeks Are sign off, Peter, upon our square blood case square. So acceleration can be written ads. I find the work. So you may right R squared G over our square plus k square and to sign or veto well, you received for five he's going to our so acceleration off by you will get our square over Irish Square, plus Ari square into G side off Twitter. It would be half off g sign or veto for surrendered he is called to are upon route to So you will get to buy three g side off Peter. So acceleration off surrender We will get now. Similarly, we have to find what spirit the radios off violation off hysterical body root off by five into art. Putting in equation One acceleration off spare you will get. It would be five by seven. The sign off Twitter. So relative acceleration if we find related acceleration between right surrender and fight is she minus a p. So this strange covered as the states covered by surrender. With respect toe five Initial velocity is zero. But directly we can write a C p in two he squared. Time is given. How much? Four tickets? No, sir. Tripping all the value g is like quite 81 sign off country and tow 40 square. So this train, scarred by surrender with respect 05 is 2.27 m. Similarly, we can calculate What? Okay, chicken clucks. Relative acceleration off cylinder with respect. Oh, spit! No! So acceleration off. Surrender minus acceleration off Despair Surrender. Having governor to buy three g Sign off. Peter minus five by seven The G. Sign off, Peter. So it will be minus one by 21 G sign off. Bitter or human? Right? Acceleration off. Sphere with respect to surrender Won by 21 g. Sign off, Peter. Now we will calculate that. Dispense covered, dispense covered Adviser. Slender with respect. Oh, sorry. Expelled with respect to surrender. Help a s C in tow. P square substituting the value one by 42 g is 9.81 signed off 20. So he signed off 10 let me see in the first case, I have to make a correction. Here it is. 10. I have written wrongly. Did you please? And fourth. But you will get distance covered by the center with respect to sarin. So the distance covered by the I spelled with respect to surrender is 564 9 m. That's all for it. Thanks for watching it.

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