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

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.)
Strength of Materials in ME mcq question image

Strength of Materials in ME mcq question image

A

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

B

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

C

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

D

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

The maximum bending moment for the beam shown in the below figure, is
Strength of Materials mcq question image

A

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

B

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

C

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

D

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

For a beam, as shown in the below figure, the maximum deflection lies at
Strength of Materials mcq question image

A

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

B

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

C

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

D

$$\sqrt {\frac{{{l^2} - {{\text{b}}^2}}}{3}} $$ 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
Strength of Materials mcq question image

A

Point A

B

Point B

C

Point C

D

Between points B and C

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
Strength of Materials mcq question image

A

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

B

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

C

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

D

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

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.
Classical Mechanics mcq question image

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

A

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

B

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

C

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

D

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

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
Strength of Materials mcq question image

A

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

B

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

C

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

D

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

The layer at the center of gravity of the beam as shown in the below figure, will be
Strength of Materials mcq question image

A

In tension

B

In compression

C

Neither in tension nor in compression

D

None of these

The lower layer of the beam as shown in the below figure, will be
Strength of Materials mcq question image

A