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Chapter 7: Problem 944

A \(2 \mathrm{~m}\) long rod of radius \(1 \mathrm{~cm}\) which is fixed from one end is given a twist of \(0.8\) radians. What will be the shear strain developed ? (A) \(0.002\) (B) \(0.004\) (C) \(0.008\) (D) \(0.016\)

Short Answer

Expert verified
(A) $0.002$ (B) $0.004$ (C) $0.008$ (D) $0.016$ Shear strain = (twist angle * (length / radius)) Shear strain = (0.8 radians) * (2 m / 0.01 m) = 0.8 * 200 = 160 None of the answer choices match the calculated shear strain of 160. Verify the exercise and answer choices for correctness.

Step by step solution

01

Convert the units

Before we can use the formula, we need to make sure all units are consistent. The radius is given in centimeters, while the length is in meters. So, let's convert the radius to meters: 1 cm = 0.01 m
02

Apply the formula

Now, we can use the formula for shear strain by plugging in the given values: Shear strain = (twist angle * (length / radius)) Shear strain = (0.8 radians) * (2 m / 0.01 m)
03

Calculate the shear strain

Perform the calculation to find the shear strain: Shear strain = (0.8 radians) * (2 m / 0.01 m) = 0.8 * 200 = 160
04

Compare with answer choices

Since none of the answer choices match the calculated shear strain of 160, there may be an error in the provided exercise or answer choices. Please verify the exercise and answer choices, and make sure they are correct.

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