Waste less time on Facebook — follow Brilliant.
×

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
6 months, 1 week ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Congratulations for being selected to represent India in ijso. Also what about JOMPC? Shivam Jadhav · 6 months, 1 week ago

Log in to reply

@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 · 6 months, 1 week ago

Log in to reply

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 · 3 months, 2 weeks ago

Log in to reply

@Shubham Dhull Cleared. Thanks anyways. P.S : your answer is correct. Rajdeep Dhingra · 3 months, 2 weeks ago

Log in to reply

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

Log in to reply

Which book is it ? John Verghese · 6 months, 1 week ago

Log in to reply

@John Verghese I don't know. Some old book for JEE subjective. Rajdeep Dhingra · 6 months, 1 week ago

Log in to reply

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 · 6 months, 1 week ago

Log in to reply

@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 · 6 months, 1 week ago

Log in to reply

@Rajdeep Dhingra If he starts from June 10 , is he will be able to clear nsejs ? He also goes to coaching ... Rahul Bubna · 6 months, 1 week ago

Log in to reply

@Rahul Bubna I think so. Rajdeep Dhingra · 6 months, 1 week ago

Log in to reply

Solution for Question 1:

Saarthak Marathe · 6 months, 1 week ago

Log in to reply

@Saarthak Marathe Thanks ! Rajdeep Dhingra · 6 months, 1 week ago

Log in to reply

@Rajdeep Dhingra You are welcome Saarthak Marathe · 6 months, 1 week ago

Log in to reply

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 · 6 months, 1 week ago

Log in to reply

@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 · 5 months ago

Log in to reply

@Rajdeep Dhingra it would be 5g/7r instead ! Shubham Dhull · 1 week, 4 days ago

Log in to reply

@Vighnesh Shenoy Thanks Rajdeep Dhingra · 6 months, 1 week ago

Log in to reply

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...