A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement of the rod axis from its original position

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Solution

Q.
A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^{5} N$ at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $θ$ of the rod axis from its original position would be: (shear moduli, $G = 10^{10} N / m^{2}$ ) [2025]

1 1/160 $π$

2 1/4 $π$

3 1/40 $π$

4 1/2 $π$

Ans.
(1)

$σ_{shear} = \frac{F}{A} = η θ$

$Shear moduli = \frac{σ_{shear}}{θ}$

$10^{10} = \frac{10^{5}}{π \times 16 \times 10^{- 4}} \times \frac{1}{θ}$

$θ = \frac{1}{160 π} Radian$

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