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The mass per unit length of a rod (length 2 m) varies as ρ = 3x kg/m. The moment of inertia (in kg m2) of the rod about a perpendicular-axis passing through the tip of the rod (at x = 0) is
- a)10
- b)12
- c)14
- d)16
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The mass per unit length of a rod (length 2 m) varies as ρ = 3x kg...
The function $\rho(x) = 2x+4$, where $x$ is measured in meters from one end of the rod. Find the mass of the rod.
We can find the total mass of the rod by integrating the density function over the length of the rod:
\begin{align*}
\text{mass} &= \int_0^2 \rho(x) dx \\
&= \int_0^2 (2x+4) dx \\
&= \left[x^2+4x\right]_0^2 \\
&= (2^2+4\cdot 2) - (0^2+4\cdot 0) \\
&= 12
\end{align*}
Therefore, the mass of the rod is 12 kg.
We can find the total mass of the rod by integrating the density function over the length of the rod:
\begin{align*}
\text{mass} &= \int_0^2 \rho(x) dx \\
&= \int_0^2 (2x+4) dx \\
&= \left[x^2+4x\right]_0^2 \\
&= (2^2+4\cdot 2) - (0^2+4\cdot 0) \\
&= 12
\end{align*}
Therefore, the mass of the rod is 12 kg.
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The mass per unit length of a rod (length 2 m) varies as ρ = 3x kg/m. The moment of inertia (in kg m2) of the rod about a perpendicular-axis passing through the tip of the rod (at x = 0) isa)10b)12c)14d)16Correct answer is option 'B'. Can you explain this answer?
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