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  4. A ball is moving in a circular path of radius 5 m. If tangential acceleration at any instant is 10 m/s2 and the net acceleration makes an angle 30 with the centripetal acceleration, then the instantaneous speed is

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Q. A ball is moving in a circular path of radius 5 m. If tangential acceleration at any instant is 10 m/s2 and the net acceleration makes an angle 30 with the centripetal acceleration, then the instantaneous speed is

MGIMS WardhaMGIMS Wardha 2009

Solution:

$ \tan \theta =\frac{{{a}_{t}}}{{{a}_{c}}}=\frac{{{a}_{t}}}{{{v}^{2}}/r} $ $ \Rightarrow $ $ {{v}^{2}}=\frac{{{a}_{t}}r}{\tan \theta } $ $ =\frac{10\times 5}{\tan {{30}^{o}}}=\frac{10\times 5}{1/\sqrt{3}} $ $ {{v}^{2}}=50\times \sqrt{3} $ $ =50\times 1.732=86.6 $ $ v=\sqrt{86.6}=9.3\,m/s $