Question

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

• A. $360\text{N}$
• B. $720\text{N}$
• C. $1440\text{N}$
• D. $2880\text{N}$

Answer 1

The correct option is C $1440\text{N}$

Initial extension will be equal to $6\text{m}$.
$\therefore$ Initial energy $=\frac{1}{2}\left(200\right)(6{)}^2=3600\text{J}$
Reaching $A:=\frac{1}{2}m{v}^2=3600\text{J}$
$\Rightarrow m{v}^2=7200\text{J}$
From F.B.D. at $A:$
$N=\frac{m{v}^2}{R}=\frac{7200}{5}=1440\text{N}$