A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\, m.$ The speed of the car at the top of the hill is between
A$16\ m/s$ and $ 17\ m/s $
B$13\ m/s$ and $14\ m/s$
C$14\ m/s$ and $15\ m/s$
D$15\ m/s$ and $ 16\ m/s$
AIPMT 2008, Medium
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C$14\ m/s$ and $15\ m/s$
c $\begin{array}{l}
\,\,\,\,\,\,\,\,\,mg = \frac{{m{v^2}}}{R} \Rightarrow v = \sqrt {Rg} \\
v = \sqrt {20 \times 10} = \sqrt {200} = 14.1m/s\\
i.e,.\,Between\,14\,and\,15\,m/s.
\end{array}$
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A block of mass $10\, kg$ is kept on a rough inclined plane as shown in the figure. A force of $3\, N$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$, such that the block does not move downward? (take $g = 10\, ms^{-2}$) ........ $N$
$Assertion$ : There is a stage when frictional force is not needed at all to provide the necessary centripetal force on a banked road.
$Reason$ : On a banked road, due to its inclination the vehicle tends to remain inwards without any chances of skidding.
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