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5.Work, Energy, Power and Collision
hard
In the given figure for $u\ =\ u_0/3$ , find the height from the ground at which the block leaves the hemisphere [where $u_0\ =\ \sqrt {\frac{{gr}}{3}} ]$
A
$\frac{{19\,r}}{9}$
B
$\frac{{19\,r}}{27}$
C
$\frac{{10\,r}}{9}$
D
$\frac{{55\,r}}{81}$
Solution
As at $\mathrm{B}$ it leaves the hemisphere,
$N=0$
$\mathrm{mg} \cos \theta=\frac{\mathrm{mV}^{2}}{\mathrm{r}}$
$\operatorname{mg} \mathrm{h} / \mathrm{r}=\frac{\mathrm{mV}^{2}}{\mathrm{r}}$
$m v^{2}=m g h \quad \ldots \ldots(1)$
By energy conservation between $A$ and $B$
$\operatorname{mgr}+\frac{1}{2} \mathrm{m}\left(\frac{\mathrm{u}_{0}}{3}\right)^{2}=\mathrm{mgh}+\frac{1}{2} \mathrm{mv}^{2}$
Put $\mathrm{u}_{0}$ and $\mathrm{mv}^{2}$
$\therefore \mathrm{h}=\frac{19 \mathrm{r}}{27}$
Standard 11
Physics
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