text: # A force P is applied at a distance ‘X’ from the end of the beam as shown in the figure. What would be value of ‘X’ so that the displacement at ‘A’ is equal to zero?
  
  This question was previously asked in
  ISRO Scientist ME 2017 Paper
  View all ISRO Scientist ME Papers >
  1. 0.5 L
  2. 0.25 L
  3. 0.33 L
  4. 0.66 L
  
  Option 4 : 0.66 L
  Free
  ISRO Scientist ME 2020 Paper
  1395
  80 Questions 240 Marks 90 Mins
  
  ## Detailed Solution
  
  Concept:
  
  FBD of diagram is
  
  The net displacement should be zero.
  
  So, displacement due to concentrated moment at B + displacement due to concentrated load P = 0
  
  displacement due to concentrated moment at B $$= \frac{{P\left( {2L - x} \right) \cdot {{\left( {2L} \right)}^2}}}{{2EI}}$$ And
  
  displacement due to concentrated load P $$=\frac{{P{{\left( {2L} \right)}^3}}}{{3EI}}$$
  
  $$\Rightarrow \frac{{P\left( {2L - x} \right) \cdot {{\left( {2L} \right)}^2}}}{{2EI}} - \frac{{P{{\left( {2L} \right)}^3}}}{{3EI}}=0$$
  
  $$\Rightarrow \frac{{P\left( {2L - x} \right) \cdot {{\left( {2L} \right)}^2}}}{{2EI}} = \frac{{P{{\left( {2L} \right)}^3}}}{{3EI}}$$
  
  $$\frac{{2L - x}}{2} = \frac{{2L}}{3}$$
  
  ⇒ 6L – 3x = 4L    ⇒ 2L = 3x
  
  $$\Rightarrow x = \frac{{2L}}{3} = 0.662$$
metadata: {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}