The density of a non-uniform rod of length 1m is given by ρ(x) = a(1+bx2) where a and b are constants and o ≤x ≤1. 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 ( 2 + b ) 3 ( 3 + b )

This is a multiple choice type question as classified in NCERT Exemplar (a) Density is given as ρ (x) = a (1+bx2) Where a and b are constant and 0 ≤ x ≤ 1 Let b=0 ρ (x) = a= constant Hence COM will be at x =0.5m Putting b=0 ain above option only a gives this answer. We should not check options by putting a=0 because ρ = 0 for a=0

The density of a non-uniform rod of length 1m is given by ρ(x) = a(1+bx²) where a and b are constants and o ≤x ≤1. The centre of mass of the rod will be at

(a) $\frac{3 (2 + b)}{4 (3 + b)}$

(b) $\frac{4 (2 + b)}{3 (3 + b)}$

(c) $\frac{3 (3 + b)}{4 (2 + b)}$

(d) $\frac{4 (2 + b)}{3 (3 + b)}$

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Payal Gupta | Contributor-Level 10

9 months ago

This is a multiple choice type question as classified in NCERT Exemplar

(a) Density is given as ρ (x) = a (1+bx²)

Where a and b are constant and 0 $\leq x \leq 1$

Let b=0 ρ (x) = a= constant

Hence COM will be at x =0.5m

Putting b=0 ain above option only a gives this answer.

We should not check options by putting a=0 b

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