The intensity of udl. which, when it acts over the entire span of 1 m of a cantilever beam of rectangular cross-section of width of 100 mm and depth 200 m, would produce a maximum shear stress of 1.5N/mm², is-

Correct option is C

​$$\text{Given: } b=100\ \text{mm},\quad d=200\ \text{mm},\quad L=1\ \text{m}=1000\ \text{mm},\quad \tau_{\max}=1.5\ \text{N/mm}^2.\\[6pt]\text{For a rectangular section: }\tau_{\max}=\frac{3}{2}\cdot\frac{V}{A},\quad A=b d.\\[6pt]A=100\times200=20000\ \text{mm}^2.\\[6pt]1.5=\frac{3}{2}\cdot\frac{V}{20000}\quad\Rightarrow\quad V=\frac{1.5\times20000\times2}{3}=20000\ \text{N}.\\[6pt]\text{For a cantilever with UDL }w\ (\text{N/m})\text{ over }L=1\ \text{m: }V_{\max}=wL=w.\\[6pt]w=V=20000\ \text{N}=20000\ \text{N/m}=20\ \text{kN/m}.$$​​