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 A mass of M kg is suspended by a weightless string.  The horizontal force that is require to displace until the string makes an angle of 450 with the initial vertical direction is   
Asked by akshaykumar999gupta | 25 Apr, 2020, 04:54: PM
answered-by-expert Expert Answer
I assume the angular displacement is 45o  not 450 as posted in question . I assume this a typo error .
 
As shown in figure, to make 45o angular displacement, the mass has to be raised vertically to a distance [ l - (l/√2) ]
 
Hence wrokdone by applied force  equals the potential energy gained by the mass
 
  F × (l/√2) = mg × [ l - (l/√2) ]
 
Hence force F  is given by
 
begin mathsize 14px style F space equals space m space g space cross times fraction numerator open square brackets l space minus space begin display style fraction numerator l over denominator square root of 2 end fraction end style close square brackets over denominator begin display style fraction numerator l over denominator square root of 2 end fraction end style end fraction space equals space m space g space cross times left parenthesis space square root of 2 space minus space 1 space right parenthesis end style
 
Answered by Thiyagarajan K | 25 Apr, 2020, 11:17: PM

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