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Question
A uniform rod of length 2L, area of cross section A and Young's modulus Y is lying at rest under the action of three forces as shown. Choose the correct statement.
A uniform rod of length 2L, area of cross section A and Young's modulus Y is lying at rest under the action of three forces as shown. Choose the correct statement.
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Solution
The correct option is C The total extension is 3FLAY.
As sum of net external force is 2F+(−F)+(−F)=0.Therefore the body is at rest and across any cross-section, net force will be zero.
By cutting cross section along B and drawing FBD it can be established that 2F force tensile in nature acts on both ends at section BC and F force tensile in nature acts in both direction at section AB.
Therefore stress in section AB is FA and extension in AB is FLAY.
The stress in section BC is 2FA and extension is given by 2FLAY.
Net extension can be algebraically added .So, total elongation will be FLAY+2FLAY =3FLAY.
As sum of net external force is 2F+(−F)+(−F)=0.Therefore the body is at rest and across any cross-section, net force will be zero.
By cutting cross section along B and drawing FBD it can be established that 2F force tensile in nature acts on both ends at section BC and F force tensile in nature acts in both direction at section AB.
Therefore stress in section AB is FA and extension in AB is FLAY.
The stress in section BC is 2FA and extension is given by 2FLAY.
Net extension can be algebraically added .So, total elongation will be FLAY+2FLAY =3FLAY.