Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
Close
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping

A thin bar of length "L" has a mass per unit length "a" that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is "b", then the distance of the centre of the mass from lighter end is ?

A thin bar of length "L" has a mass per unit length "a" that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is "b", then the distance of the centre of the mass from lighter end is ?

Grade:12

2 Answers

Sanchayan Ghosh
27 Points
7 years ago
So this is how you do it. Imagine that the left end of the rod has a mass per unit length of b, which increases to the right end as a. Consider a small element dx at a distance x from the lighter end. let mass per unit length be ? now, ? a x. therefore, ? = kx. at the heavier end, ? = a. so, a = kL. or, k = a/L Now, centre of mass = 1/M (? xdm). dm = ?dx. dm = kxdx. therefore, xdm = x^2dx Integrating and taking limits 0 to L. ? xdm =k ? x^2dx = x^3 /3 So, simplifying, we get, distance of centre of mass = 1/M (a/L) (L^3/3) = a(L^2/3M). Since the mass of the rod is given: b becomes unnecessary.
Abhijeet
12 Points
7 years ago
Thanx !

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Register ICAT

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