A massless uniform rod is subjected to force F at its free end as shown in figure

Question

A massless uniform rod is subjected to force F at its free end as shown in figure. The ratio of tensile stress at plane $P_{1}$ to stress at $P_{2}$ is

Smart Achievers · Accepted Answer

(3)

$At P_{2}, Stress = S_{2} = \frac{F}{A}$

$At P_{1}, Stress = S_{1} \times \frac{F \cos 60 °}{\frac{A}{\cos 60 °}} = \frac{F}{4 A}$

$\Rightarrow \frac{S_{1}}{S_{2}} = \frac{1}{4}$

Solution

Q.
A massless uniform rod is subjected to force F at its free end as shown in figure. The ratio of tensile stress at plane $P_{1}$ to stress at $P_{2}$ is

1 1 : 2

2 $\sqrt{2}$ : 1

3 1 : 4

4 3 : 2

Ans.
(3)

$At P_{2}, Stress = S_{2} = \frac{F}{A}$

$At P_{1}, Stress = S_{1} \times \frac{F \cos 60 °}{\frac{A}{\cos 60 °}} = \frac{F}{4 A}$

$\Rightarrow \frac{S_{1}}{S_{2}} = \frac{1}{4}$

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