The engine of a train passes an electric pole with a velocity ‘u’ and the last compartment of the train crosses the same pole with a velocity v. Then the velocity with which the mid-point of the train passes the pole is

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$\frac{u + v}{2}$

$\sqrt{\frac{u^{2} + v^{2}}{2}}$

answer is D.

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Detailed Solution

Let l be the total length of the train and v ' be the velocity of the midpoint of train
$v^{' 2} - u^{2} = 2 a \frac{l}{2} (i) v^{2} - v^{' 2} = 2 a \cdot \frac{l}{2} (ii) From (1) and (2) we get v^{'} = \sqrt{\frac{v^{2} + u^{2}}{2}}$

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