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A uniform rod of mass m, length L, area of cross section A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity ω in a horizontal plane. If Y is the Young's modulus of the material of the rod, the increase in its length due to rotation of rod is

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Important Questions on Mechanical Properties of Solids

MEDIUM
JEE Main/Advance
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A circular wire of radius R, placed on a horizontal surface is made to rotate about a fixed vertical axis passing through its center as shown. If breaking stress of the material of wire is S0, then find maximum value of ω so that wire does not break (Cross-sectional area of wire is A,λ is the linear mass density of wire)

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MEDIUM
JEE Main/Advance
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Consider an arrangement shown in the diagram which is combination of two rods (1) and (2). Their length, cross-sectional area and Young's modulus are shown in diagram. If force F0 is applied at end Q of rod (2), then total elongation of combined system is [ P is the common end of rod (1) and (2)]

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HARD
JEE Main/Advance
IMPORTANT

Consider a metal rod shown in figure. Two forces are applied at the ends of the rod. Find displacement of point P

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MEDIUM
JEE Main/Advance
IMPORTANT

A metallic rod of cross-sectional area A is subjected to equal and opposite tensile forces F at its ends as shown in figure. Consider a plane xx' making an angle θ as indicated in figure. For what value of $\theta$ is the shearing stress on plane xx' is maximum?

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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.

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Select the correct alternatives.

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Two thin wires A and B of equal length L and equal cross-sectional area A and masses M1 and M2 respectively are joined end to end and suspended as shown in the figure. Wires A and B have Young's modulus Y1 and Y2 respectively. The total elongation in the combined wire is

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MEDIUM
JEE Main/Advance
IMPORTANT
A uniform ring of mass M and radius R is made of thin wire of cross-sectional area A and Young's modulus Y. The ring is rotated about its axis with constant angular speed ω. The elongation produced in the wire is