A small body slips, subject to the force of friction, from point $A$ to point $B$ along two curved surfaces of equal radius, first along route $1,$ then along route $2$. Friction does not depend on the speed and the coefficient of friction on both routes is the same. In which case will the body’s speed at $B$ be greater?
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Normal in case $2>$ Normal in case $1$ Friction $\propto$ Normal
$\mathrm{mg} \cos \theta-\mathrm{N}_{1}=\frac{\mathrm{mu}^{2}}{\mathrm{r}}$
$\mathrm{N}_{1}=\mathrm{mg} \cos \theta-\frac{\mathrm{mv}^{2}}{\mathrm{r}}$
$\mathrm{N}_{2}-\mathrm{mg} \cos \theta=\frac{\mathrm{mu}^{2}}{\mathrm{r}}$
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