A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle \(\theta_{1}\) . In the next 2 sec, it rotates through an additional angle \(\theta_{2}\) . The ratio of \(\sqrt{3mg}\) is
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Using relation \(r = r_0 t + \frac{1}{2} a t^2\)
\(r_1 = \frac{1}{2} \{ v_1 (2)^2 - 2v \}\) …(i) (As \(r_{wc} \quad 0, t \quad 2 \, \mathrm{sec}\) )
Now using same equation for t = 4 sec, w 0 = 0
\(v_1 + v_2 = -\frac{1}{2}n(4)^2 - 8n\) …(ii)
From (i) and (ii), \(r_1 \quad 2x\) and \(\omega_2 \quad 6ct\) \ \ \(\frac{p'_2}{p_1} = .3\)
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