question_answer

If acceleration and velocity of a particle are \[5\,m{{s}^{-2}}\hat{j}\] and \[3\hat{i}+4\hat{j}\,\,m{{s}^{-1}}\] respectively then centripetal acceleration and radius of current are at that point of the path where particle is present will be :

A)  \[3\,m{{s}^{-2}},\frac{3}{25}m\]    

B) \[4m{{s}^{-2}},\frac{4}{25}m\]

C) \[5m{{s}^{-2}},\frac{1}{25}m\]                

D)  None

Correct Answer: A

Solution :

  Velocity is always directed along the tangent of its path hence component of acceleration along velocity is tangential acceleration and perpendicular to it is radial or centripetal acceleration. \[{{a}_{c}}=a\sin 37{}^\circ =5\times \frac{3}{5}=3=\frac{{{v}^{2}}}{r}\Rightarrow t=\frac{3}{25}\]