Question

A train has each compartment of mass $‘m^{\prime }$ is accelerating uniformly. The velocity of the engine is $V_1$ and the velocity of the last compartment is $V_2$. Find the velocity of the compartment in the middle when it passes the same mile marker assuming that the compartments are of point sizes.

• A. $\sqrt{\frac{V_1^2-V_2^2}{2}}$
• B. $\sqrt{\frac{V_1^2+V_2^2}{2}}$
• C. $\frac{V_1^2-V_2^2}{2}$
• D. $\frac{V_1^2+V_2^2}{2}$

Answer 1

The correct option is B $\sqrt{\frac{V_1^2+V_2^2}{2}}$


For the portion AC,
$V^2-V_1^2=2ax$
For the portion CB
$V_2^2=V^2=2ax$
$\Rightarrow V=\sqrt{\frac{V_1^2+V_2^2}{2}}$