Question

Set up but do not evaluate an integral to compute the mass of a

thin metal rod oriented on the x-axis, given that its linear mass
density is rho(x)=3x^2−x+2 grams per centimeter.

Answer 1

>>Physics

>>Systems of Particles and Rotational Motion

>>Problems on Centre of Mass

>>A rod of length l has an non - uniform l

Question



A rod of length l has an non-uniform linear mass density given by ρ(x)=a+b(lx)2, where a and b are constants and 0≤x≤l. The value of x for the centre of mass of the rod is at:

A

34(2a+3ba+b)l

B

23(3a+b2a+b)l

C

43(3a+b2a+b)l

D

23(2a+ba+b)l

Medium

JEE Mains

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Updated on : 2022-09-05

Solution



Verified by Toppr

Correct option is C)

Given, λ=(a+b(lx)2)

dxd

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Class 11

>>Physics

>>Systems of Particles and Rotational Motion

>>Problems on Centre of Mass

>>A rod of length l has an non - uniform l

Question



A rod of length l has an non-uniform linear mass density given by ρ(x)=a+b(lx)2, where a and b are constants and 0≤x≤l. The value of x for the centre of mass of the rod is at:

A

34(2a+3ba+b)l

B

23(3a+b2a+b)l

C

43(3a+b2a+b)l

D

23(2a+ba+b)l

Medium

JEE Mains

Open in App

Updated on : 2022-09-05

Solution



Verified by Toppr

Correct option is C)

Given, λ=(a+b(lx)2)

dxd



Use app

Login

Class 11

>>Physics

>>Systems of Particles and Rotational Motion

>>Problems on Centre of Mass

>>A rod of length l has an non - uniform l

Question



A rod of length l has an non-uniform linear mass density given by ρ(x)=a+b(lx)2, where a and b are constants and 0≤x≤l. The value of x for the centre of mass of the rod is at:

A

34(2a+3ba+b)l

B

23(3a+b2a+b)l

C

43(3a+b2a+b)l

D

23(2a+ba+b)l

Medium

JEE Mains

Open in App

Updated on : 2022-09-05

Solution



Verified by Toppr

Correct option is C)

Given, λ=(a+b(lx)2)

dxd