Question

A collar $B$ of mass $2\, kg$ is constrained to move along a horizontal smooth and fixed circular track of radius $5\, m$. The spring lying in the plane of the circular track and having spring constant $200\, Nm ^{-1}$ 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. 360 N
• B. 720 N
• C. 1440 N
• D. 2880 N

Answer 1

Answer: (C)

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