question_answer

            A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure).  When released  from initial horizontal position, its instantaneous angular acceleration will be- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) \[\frac{g}{13l}\]            

B) \[\frac{g}{2l}\]

C) \[\frac{g}{3l}\]              

D)                  \[\frac{7g}{3l}\]

Correct Answer: A

Solution :

\[\tau \,\,about\,\,P=5\,\,{{M}_{0}}g\,\ell \,\,2\,{{M}_{0}}g\,\times \,2\ell \] \[={{M}_{0}}g\,\ell \] \[\tau \,\,about\text{ }P={{I}_{p\alpha }}\] \[{{M}_{0}}g\,\ell =\left[ 5\,{{M}_{0}}{{\ell }^{2}}+2{{M}_{0}}\,\times \,4{{\ell }^{2}} \right]\alpha \] \[{{M}_{0}}g\,\ell \,\,=\,\,13\,{{M}_{0}}{{\ell }^{2}}\alpha \] \[\alpha =\frac{g}{13\,\ell }\]