A thin uniform stick of length l and mass m is held horizontally … - Vidyadip

MCQ

A thin uniform stick of length $l$ and mass $m$ is held horizontally with its end $B$ hinged on the edge of a table. Point $A$ is suddenly released. The acceleration of the centre of mass of the stick at the time of release, is

✓
$\frac{3}{4}\,g$
B
$\frac{3}{7}\,g$
C
$\frac{2}{7}\,g$
D
$\frac{1}{7}\,g$

✓

Answer

Correct option: A.

$\frac{3}{4}\,g$

a
$\tau=\operatorname{mg} \times \frac{\ell}{2} \quad$ and $\tau=I \alpha$

also $a$ $=\alpha r$

$=\frac{\tau}{\mathrm{I}} \times \frac{\ell}{2}=\frac{\mathrm{mg}}{\frac{\mathrm{m} \ell^{2}}{3}} \times \frac{\ell}{2} \times \frac{\ell}{2}=\frac{3}{4} \mathrm{g}$

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