0

Guest

Courses New

A semicircular portion of radius 'r' is cut from a uniform rectangular plate as shown in figure. The distance of centre of mass 'C' of remaining plate, from point O is... (see attachment)

A semicircular portion of radius 'r' is cut from a uniform rectangular plate as shown in figure. The distance of centre of mass 'C' of remaining plate, from point O is... (see attachment) 

Question Image
Grade:12

2 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

Distance of center of mass of semicircular disc from the center of disc of radius r is\dfrac{4r}{3\pi}

Hence distance of center of mass of the carved plate is (assuming\sigmato be the mass per unit area)

\dfrac{(\sigma .2r^2)(\dfrac{r}{2})+(-\sigma . \dfrac{\pi r^2}{2})(\dfrac{4r}{3\pi})}{\sigma(2r^2-\dfrac{\pi r^2}{2})}=\dfrac{2r}{3(4-\pi)}
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem below.
 
Let us assume the complete figure into two fragments- a complete rectangular plate + a semi circular plate with negative mass ( or area).
Area of rectangular plate = r x 2r = 2r2
Area of semi circular plate = – πr2/2
Now, CM of rectangular region will be at C i.e. at r/2 from O.
Now, CM of circular plate = 4r/3π
 
Hence CM of the remaining portion = [2r2 x r/2 + (– πr2/2) x 4r/3π] / [2r2 – πr2/2]
= (r – 2r/3)/(2 – π/2) = 2r/3(4 – π)
 
Hence option (D) is correct.
 
Thanks and regards,
Kushagra

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More