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Doubts ! Help Needed

Please give a solution to the below questions.

  1. Please help

    Please help

  2. Please help

    Please help

Note by Rajdeep Dhingra
10 months ago

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Congratulations for being selected to represent India in ijso. Also what about JOMPC? Shivam Jadhav · 10 months ago

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@Shivam Jadhav Thanks. It will be out day after tomorrow. I have marked all the solutions I'll compile and post it on monday. Rajdeep Dhingra · 10 months ago

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Which book is it? Ritik Gandhi · 1 month, 2 weeks ago

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@Ritik Gandhi I answered it before also , an old JEE subjective book. Just Mechanics for JEE is written on the book , nothing else. Rajdeep Dhingra · 1 month, 2 weeks ago

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@Rajdeep Dhingra who's the author of the book? Ritik Gandhi · 1 month, 2 weeks ago

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@Ritik Gandhi ?? Ritik Gandhi · 4 weeks ago

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Bro is your second doubt cleared ? i am getting it's answer as root 5g/7(R-r) tell if not cleared i will give the solution ( if my answer is correct.) . Shubham Dhull · 7 months, 1 week ago

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@Shubham Dhull Cleared. Thanks anyways. P.S : your answer is correct. Rajdeep Dhingra · 7 months, 1 week ago

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Hey @Rajdeep Dhingra why not coming to fiitjee ? PLease tell the truth !! Parth Bhardwaj · 7 months, 3 weeks ago

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Which book is it ? John Verghese · 10 months ago

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@John Verghese I don't know. Some old book for JEE subjective. Rajdeep Dhingra · 10 months ago

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Hy rajdeep, can u give some tips for prepartion of nsejs , as my brother will be giving this year, presently he is in class 9. Rahul Bubna · 10 months ago

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@Rahul Bubna Read 9th and 10th class NCERT books thoroughly , if possible read 11th and 12th class NCERT also.(only relevant topics). For NSEJS most important is your speed of solving questions. Rajdeep Dhingra · 10 months ago

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@Rajdeep Dhingra If he starts from June 10 , is he will be able to clear nsejs ? He also goes to coaching ... Rahul Bubna · 10 months ago

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@Rahul Bubna I think so. Rajdeep Dhingra · 10 months ago

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Solution for Question 1:

Saarthak Marathe · 10 months ago

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@Saarthak Marathe Thanks ! Rajdeep Dhingra · 10 months ago

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@Rajdeep Dhingra You are welcome Saarthak Marathe · 10 months ago

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Question 2:
Let \( f \)denote the friction force acting on the body. Now, ablut the center of mass writing the torque equation,
\( f \cdot r = \dfrac{MR^{2}\alpha}{2} \)
\( f = \dfrac{MR\alpha}{2} \)
But since the cylinder doesn't slip \( r \alpha = a_{cm} \)
\( f = \dfrac{ma_{cm}}{2} \) Now,
\( mg\sin(\theta) - f = ma_{cm} \)
\( mg\sin(\theta) = \dfrac{3ma_{cm}}{2} \)
\( a_{cm} = \dfrac{2g\sin(\theta)}{3} \)
\( \alpha = \dfrac{2g \sin(\theta)}{3r} \)
For small values of \( \theta \), \( \sin(\theta) \approx \theta \)
\( \alpha = - \dfrac{2g \theta}{3r} \)
The negative sign just denotes that direction of alpha is opposite to displacement.
This is the rotational analogue of \( a = -\omega^{2}x \)
\( \therefore \omega = \sqrt{\dfrac{2g}{3r}} \)
Frequency \( \dfrac{\omega}{2\pi} = \dfrac{1}{2\pi} \sqrt{\dfrac{2g}{3r}} \) Vighnesh Shenoy · 10 months ago

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@Vighnesh Shenoy It is wrong bro. \( \theta\) is the angle you moved the center of mass not the angle by which you rotated the sphere. Hence you can't equate \( {\omega}^2 \) to \(\dfrac{2g}{3r}\). Rajdeep Dhingra · 8 months, 4 weeks ago

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@Rajdeep Dhingra it would be 5g/7r instead ! Shubham Dhull · 4 months ago

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@Vighnesh Shenoy Thanks Rajdeep Dhingra · 10 months ago

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