Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.
(N/A) The equation for the bending of a beam (or rod) is given by the relation: $M = \frac{Y I_g}{R}$,where $M$ is the bending moment,$Y$ is Young's modulus of the material,$I_g$ is the geometrical moment of inertia of the cross-section about the neutral axis,and $R$ is the radius of curvature of the neutral axis.
The bending moment $M$ is defined as the product of force and distance,so its $SI$ unit is $N \cdot m$ (Newton-meter).
The dimensional formula for the bending moment is $[M^1 L^2 T^{-2}]$.
The bending moment $M$ is defined as the product of force and distance,so its $SI$ unit is $N \cdot m$ (Newton-meter).
The dimensional formula for the bending moment is $[M^1 L^2 T^{-2}]$.
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One end of a metal wire is fixed to a ceiling and a load of $2 \ kg$ hangs from the other end. $A$ similar wire is attached to the bottom of the load and another load of $1 \ kg$ hangs from this lower wire. Then the ratio of longitudinal strain of the upper wire to that of the lower wire will be . . . . . . .
[Area of cross section of wire $= 0.005 \ cm^2$,$Y = 2 \times 10^{11} \ Nm^{-2}$ and $g = 10 \ ms^{-2}$]
[Area of cross section of wire $= 0.005 \ cm^2$,$Y = 2 \times 10^{11} \ Nm^{-2}$ and $g = 10 \ ms^{-2}$]
DifficultJEE MAIN 2024
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