Properties of Matter 1 Question 17

17. A uniform rod of length $L$ and density $\rho$ is being pulled along a smooth floor with a horizontal acceleration $\alpha$ (see figure). The magnitude of the stress at the transverse cross-section through the mid-point of the rod is ………. .

(1993, 1M)

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Answer:

Correct Answer: 17. $\frac{\rho L \alpha}{2}$

Solution:

  1. Let $A$ be the area of cross-section of the rod. FBD of rod at mid-point

Mass $m=$ volume $\times$ density

$$ =\left(\frac{L}{2} \cdot A\right) \rho $$

$\therefore \quad T=m \alpha=\left(\frac{L}{2} A \rho \alpha\right)$

$\therefore$ Stress $=\frac{T}{A}=\frac{1}{2} \rho \alpha L$



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