The density of a non-uniform rod of length 1m is given by rho- -x- - a-1-bx 2- where a and b are constants and 1 ox le- le- - The centre of mass of the rod will be at-a-3-2-b-4-3-b-b-4-2-b-3-3-b-c-3-3-b-4-2-b-d-4-3-b-3-2-b-explain how to solve-

nbsp;Center of mass is given by c.o.m=1/M int;x rho; (x )dx total mass of the rod will be obtaind by itegrating rho; (x ) from 0 to L M= int;a(1+b ...

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Standard XII

Chemistry

Friedel Crafts Alkylation, Acylation

The density o...

Question

The density of a non-uniform rod of length 1m is given by ρ (x) = a(1+bx 2) where a and b are constants and 1 ox ≤≤ . The centre of mass of the rod will be at
(a)3(2+b)/4(3+b)(b)4(2+b)/3(3+b)(c)3(3+b)/4(2+b)(d)4(3+b)/3(2+b)explain how to solve?

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Solution

Center of mass is given by
c.o.m=1/M ∫x ρ (x )dx
total mass of the rod will be obtaind by itegrating ρ (x ) from 0 to L
M=∫a(1+bx²)dx from 0-L
aL+bL³/3
now,
com={1/( aL+baL³/3) }*∫X a(1+bx²) dx
(aL²/2+abL⁴/4 )/ ( aL+baL³/3)
here L=1 given
com=3(2+b)/4(3+b) answer

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Similar questions

Q. The density of a non-uniform rod of length 1m is given by

ρ (x) = a (1 + {b x}^{2})

where a and b are constants and 0

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The density of a non-uniform rod of length 1m is given by ρ (x) = a(1+bx 2) where a and b are constants and 1 ox ≤≤ . The centre of mass of the rod will be at(a)3(2+b)/4(3+b)(b)4(2+b)/3(3+b)(c)3(3+b)/4(2+b)(d)4(3+b)/3(2+b)explain how to solve?

Center of mass is given by c.o.m=1/M ∫x ρ (x )dx total mass of the rod will be obtaind by itegrating ρ (x ) from 0 to L M=∫a(1+bx2)dx from 0-L aL+bL3/3 now, com={1/( aL+baL3/3) }*∫X a(1+bx2) dx (aL2/2+abL4/4 )/ ( aL+baL3/3) here L=1 given com=3(2+b)/4(3+b) answer

The density of a non-uniform rod of length 1m is given by ρ (x) = a(1+bx 2) where a and b are constants and 1 ox ≤≤ . The centre of mass of the rod will be at
(a)3(2+b)/4(3+b)(b)4(2+b)/3(3+b)(c)3(3+b)/4(2+b)(d)4(3+b)/3(2+b)explain how to solve?

Center of mass is given by
c.o.m=1/M ∫x ρ (x )dx
total mass of the rod will be obtaind by itegrating ρ (x ) from 0 to L
M=∫a(1+bx²)dx from 0-L
aL+bL³/3
now,
com={1/( aL+baL³/3) }*∫X a(1+bx²) dx
(aL²/2+abL⁴/4 )/ ( aL+baL³/3)
here L=1 given
com=3(2+b)/4(3+b) answer