AP EAMCET · PHYSICS · Motion In One Dimension
If the engine of a long train moving with constant acceleration crosses a tree with velocity ' \(u\) ' and the last compartment of the train crosses the same tree with velocity ' \(v\) ', then the velocity with which the middle compartment crosses the same tree is
- A \(\frac{(v+u)}{2}\)
- B \(\frac{2 u v}{(u+v)}\)
- C \(\sqrt{\frac{\left(v^2+u^2\right)}{2}}\)
- D \(\sqrt{2\left(u^2+v^2\right)}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{\left(v^2+u^2\right)}{2}}\)
Step-by-step Solution
Detailed explanation
Using equation of motion, \(\mathrm{v}^2-\mathrm{u}^2=2 \mathrm{as}\) let the length of train is L, on rearranging \(v^2-u^2=2 a L\) \(a=\frac{v^2-u^2}{2 L}\) ....(1) The velocity with which middle compartment crosses pain, is given by,…
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