The density of a non-uniform rod of length 1 m is given by ρ(x)=a(1+b x2) where a and b are constants and 0 ≤ x ≤ 1. The centre of mass of the rod will be at

Question

The density of a non-uniform rod of length 1 m is given by ρ(x)=a(1+b x2) where a and b are constants and 0 ≤ 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(3+b)/3(2+b))

Tardigrade Admin · Accepted Answer

When b arrow 0, the density becomes uniform and hence the cetnre of mass is at x=0.5. Only option (a) tends to 0.5 as b arrow 0.

Q. The density of a non-uniform rod of length $1 m$ is given by
$ρ (x) = a (1 + b x^{2})$
where $a$ and $b$ are constants and $0 \leq x \leq 1$ .
The centre of mass of the rod will be at

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

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

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

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

When $b \to 0$ , the density becomes uniform and hence the cetnre of mass is at $x = 0.5$ . Only option (a) tends to $0.5$ as $b \to 0$ .

Q. 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 0≤x≤1. The centre of mass of the rod will be at

4(3+b)3(2+b)​

3(3+b)4(2+b)​

4(2+b)3(3+b)​

3(2+b)4(3+b)​