The density of a non-uniform rod of length 1m is given by rho (x)=a (1+bx^(2)) where, a and b are constant and 0 le x le 1. The centre of mass of the rod will be at

The density of a non-uniform rod of length 1m is given by rho (x)=a (1

1.	The density of a non-uniform rod of length 1m is given by rho (x)=a (1+bx^(2)) where, a and b are constant and 0 le x le 1. The centre of mass of the rod will be at
Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>(2+<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>))/(4(3b+b))`<br/>`(4(2+b))/(3(3+b))`<br/>`(3(3+b))/(4(2+b))`<br/>`(4(3+b))/(3(2b+b))`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :Density is given as `rho (x) = a (1+bx^(2))` <br/> where a and b are constants and `0 le x le 1` <br/> <a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> `b rarr 0`, in this case <br/> `rho (x) = a=` constant <br/> Hence, centre of mass will be at `x=0.5` m (<a href="https://interviewquestions.tuteehub.com/tag/middle-1096062" style="font-weight:bold;" target="_blank" title="Click to know more about MIDDLE">MIDDLE</a> of the rod) Putting, `b=0` in all the options, only (a) given 0.5. <br/> Note : We should not check options by putting `a=0`, because `rho = 0` for a = 0.</body></html>