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JEE Main 201219 MayOnline
Exam
JEE Main
Year
2012
Date
19 May
Mode
Online
Subject
Physics
Chapter
Motion in One Dimension

JEE Main 2012 · 19 May · Online · Physics · Motion in One Dimension

A goods train accelerating uniformly on a straight railway track,...

A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity uu and the guard's room passes with velocity vv. The middle wagon of the train passes the pole with a velocity.

Options

  1. Au+v2\frac{u+v}{2}
  2. B12u2+v2\frac{1}{2} \sqrt{u^2+v^2}
  3. Cuv\sqrt{u v}
  4. D\sqrt{\left(\frac{u^2+v^2}{2}\right)}

Correct answer

D. \sqrt{\left(\frac{u^2+v^2}{2}\right)}

Step-by-step solution

Let ' SS ' be the distance between two ends ' aa ' be the constant acceleration As we know V2−u2=2aSV^2-u^2=2 a S or, aS=V2−u22a S=\frac{V^2-u^2}{2} Let VV be velocity at mid point. Therefore, Vc2−u2=2aS2V_c^2-u^2=2 a \frac{S}{2}Vc2=u2+aSVc2=u2+V2−u22Vc=u2+v22\begin{aligned}& V_c^2=u²+a S \\ & V_c^2=u²+\frac{V^2-u^2}{2}\\ & V_c=\sqrt{\frac{u^2+v^2}{2}} \end{aligned}$$
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