For a beam, as shown in the below figure, the deflection at C is (where E = Young's modulus for the beam material and $$I$$ = Moment of inertia of the beam section.)<br><img src="/images/question-image/mechanical-engineering/strength-of-materials-in-me/1661769528-for-a-beam-the-deflection-at-c-is-where-e.jpg" title="Strength of Materials in ME mcq question image" alt="Strength of Materials in ME mcq question image">

$$\frac{{{\text{W}}{l^3}}}{{48{\text{E}}I}}$$

$$\frac{{{\text{W}}{{\text{a}}^2}{{\text{b}}^2}}}{{3{\text{E}}Il}}$$

$$\frac{{{\text{Wa}}}}{{{\text{a}}\sqrt 3 {\text{E}}Il}} \times {\left( {{l^2} - {{\text{a}}^2}} \right)^{\frac{3}{2}}}$$

$$\frac{{5{\text{W}}{l^3}}}{{384{\text{E}}I}}$$

Correct Answer: $$\frac{{{\text{W}}{{\text{a}}^2}{{\text{b}}^2}}}{{3{\text{E}}Il}}$$

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.

The moment of inertia of the resulting body about Y-axis is

$$\frac{{\pi \rho {R^5}}}{4}$$

$$\frac{{5\pi \rho {R^5}}}{{12}}$$

$$\frac{{7\pi \rho {R^5}}}{{12}}$$

$$\frac{{3\pi \rho {R^5}}}{4}$$

A torsional system with discs of moment of inertia $${I_1}$$ and $${I_2}$$ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is 'G'. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to

$${\text{G}} \times {I_2}$$

$${{\text{G}}^2} \times {I_2}$$

$$\frac{{{I_2}}}{{\text{G}}}$$

$$\frac{{{I_2}}}{{{{\text{G}}^2}}}$$

For a beam, as shown in the below figure, when the load W is applied in the center of the beam, the maximum deflection is

$$\frac{{{\text{W}}{l^3}}}{{48{\text{E}}I}}$$

$$\frac{{5{\text{W}}{l^3}}}{{384{\text{E}}I}}$$

$$\frac{{{\text{W}}{l^3}}}{{392{\text{E}}I}}$$

$$\frac{{{\text{W}}{l^3}}}{{384{\text{E}}I}}$$

For a beam, as shown in the below figure, the maximum deflection lies at

$$\frac{l}{3}$$ from B

$$\frac{l}{3}$$ from A

$$\sqrt {\frac{{{l^2} - {{\text{a}}^2}}}{3}} $$ from B

$$\sqrt {\frac{{{l^2} - {{\text{b}}^2}}}{3}} $$ from A

A simply supported beam of length 'l' carries a point load 'W' at a point C as shown in the below figure. The maximum deflection lies at

Point A

Point B

Point C

Between points B and C

The maximum bending moment for the beam shown in the below figure, lies at a distance of ________ from the end B.

$$\frac{l}{2}$$

$$\frac{l}{3}$$

$$\frac{l}{{\sqrt 2 }}$$

$$\frac{l}{{\sqrt 3 }}$$

The maximum bending moment for the beam shown in the below figure, is

$$\frac{{{\text{w}}{l^2}}}{{3\sqrt 3 }}$$

$$\frac{{{\text{w}}{l^2}}}{{6\sqrt 3 }}$$

$$\frac{{{\text{w}}{l^2}}}{{9\sqrt 3 }}$$

$$\frac{{{\text{w}}{l^2}}}{{12\sqrt 3 }}$$

A simply supported beam with a gradually varying load from zero at ‘B’ and ‘w’ per unit length at ‘A’ is shown in the below figure. The shear force at ‘B’ is equal to

$$\frac{{{\text{w}}l}}{6}$$

$$\frac{{{\text{w}}l}}{3}$$

$${\text{w}}l$$

$$\frac{{2{\text{w}}l}}{3}$$

For the beam shown in the below figure, the shear force diagram between A and B is

A horizontal line

A vertical line

An inclined line

A parabolic curve

The layer at the center of gravity of the beam as shown in the below figure, will be

In tension

In compression

Neither in tension nor in compression

None of these