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Model Paper 3 — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsModel Paper 35 Marks
Question
A metre scale AB is held vertically with its one end A on the floor and is then allowed to fall. Find the speed of the other end B when it strikes the floor, assuming that the end on the floor does not slip.
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Answer

Let $M$ be the mass and Lbe the length of the metre scale. When the upper end of the rod strikes the floor, its centre of gravity falls through height $\frac{L}{2}$.
Image
M.I. of the scale about the lower end $A, I=$ M.I. of the scale about the parallel axis through $C G+M d_2$
$
=I_0+M d^2=\frac{M L^2}{12}+\frac{M L^2}{4}=\frac{M L^2}{3} \quad\left[\because d=\frac{L}{2}\right]
$
Also, $\omega=\frac{v}{r}=\frac{v}{L}$
Gain in rotational K.E.
$
=\frac{1}{2} I \omega^2=\frac{1}{2} \cdot \frac{M L^2}{3} \cdot \frac{v^2}{L^2}=\frac{M v^2}{6}
$
Now, Gain in rotational K.E. $=$ Loss in P.E.
$
\frac{M v^2}{6}=M g \cdot \frac{L}{2} \quad \text { or } \quad v^2=3 g l
$
or $v=\sqrt{3 g L}=\sqrt{3 \times 9.8 \times 1}=5.4 ms^{-1}$

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