Question

Figure shows a frictionless track at which a slider starts from rest at point $A$. Find the minimum value for the radius of curvature of track at point $B$, such that the slider remains in contact with the track.

• A. $20\text{m}$
• B. $10\text{m}$
• C. $40\text{m}$
• D. $25\text{m}$

Answer 1

The correct option is A $20\text{m}$

From the law of conservation of mechanical energy between points $A$ and $B$,
Loss in potential energy $=$ Gain in kinetic energy
$\Rightarrow mgh=\frac{1}{2}m{v}^2$
$\Rightarrow v^2=2gh$ .............$\left(1\right)$
Here $h$ is the height difference between point $A$ and $B$.


At point $B$,
$mg-N=\frac{m{v}^2}{r}$
In critical case, $N=0$,
$v^2=rg$
$\Rightarrow 2gh=rg$ $[$ from $\left(1\right)]$
$\Rightarrow r=2h$
$\Rightarrow r=2\times 10=20\text{m}$ $[$ from diagram $]$