Centre of mass of non-uniform rod

[carlyn medona]

Homework Statement

The mass of non uniform rod increases linearly with distance from lighter end. If m is mass of the rod and l it's total length a the linear density at lighter end, then found the distance of centre of mass from lighter end

Homework Equations

I put λ= kx+a where lands is linear density k a constant and x the distance from lighter end and integrated but can't get the answer in terms of m l and a

The Attempt at a Solution

 

[kuruman]

Please show us what you did.

 

[carlyn medona]

So how do I eliminate k from the equation

 

[kuruman]

Remember that m = ∫(kx+a)dx

 

[carlyn medona]

I think I made a mistake in my first calculation , is this one right?

 

[Abhishek kumar]

I think I made a mistake in my first calculation , is this one right?

Yes this looks right.

 

[carlyn medona]

Thanks for checking

 

[Ray Vickson]

So how do I eliminate k from the equation

For future reference: you should not post images of handwritten work; actually take the time and trouble to type things out. Most helpers will not even look at all at such posted images, but you were lucky in this case to get a sympathetic reader. Please consult the post "Guidelines for students and helpers" by Vela, pinned to the start of this forum's file list.

 

[carlyn medona]

Oops sorry for that.