Classical Mechanics
# Circular Motion

A boy runs on a circular path of radius \( R=28\text{ meters}\) with constant speed \(u=4 \text{ m/s}\).

Another boy starts from the center of the circle to catch the first boy. The second boy always moves towards the first one. and maintains a speed of \(v = 4\text{ m/s}\). How long will the chase last in seconds?

**Details and Assumptions**:

1) Ignore air friction.

2) Take \(\pi = \dfrac{22}7\).

A rope loop of radius \(r = \SI[per-mode=symbol]{0.1}{\meter}\) and mass \(m = 50\pi\,\text{g}\) rotates on a frictionless table such that the tangential velocity of any point on the loop is \(v_\textrm{tangential}=\SI[per-mode=symbol]{6}{\meter\per\second}.\)

Find the tension in the loop (in Newtons).

\[a_N=\frac{cvR}{(2Rt-vt^2)} \quad , \quad a_T=\frac{R(vt-R)v^{\frac{d}{e}}}{(2Rt-vt^2)^{\frac{f}{g}}}\].

Find \(|c|+|d|+|e|+|f|+|g|\)

**Details and Assumptions**

As shown in figure \(v\) is the constant along \(AB\).

Given Figure is top view of the setup.

\(c,d,e,f,g\) are natural numbers and \(\frac{d}{e} ,\frac{f}{g}\) are in simplest forms.

\(a_N,a_T \) represent normal and tangential accelerations respectively.

you can neglect minus sign in accelerations due to directions.

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