Question

A collar $B$ of mass $2kg$ is constrained to move along a horizontal smooth and fixed circular track of radius $5m$. The spring lying in the plane of the circular track and having spring constant $200N{m}^{-1}$ is undeformed when the collar is at $A$. If the collar starts from rest at $B$, the normal reaction exerted by the track on the collar when it passes through $A$ is

• A. $360N$
• B. $720N$
• C. $1440N$
• D. $2880N$

Answer 1

The correct option is C $1440N$

Using energy conservation

the length of the spring at position B is =$\sqrt{5^2+{12}^2}=13m$

And the natural length is $7m$

Therefore the extension in the spring $13-7=6m$

$\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2⟹m{v}^2=200\times 6^2$

From FBD of collar at A

$N=\frac{m{v}^2}{r}=\frac{200\times 36}{5}=1440N$

Hence Option C is correct