A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45° with the initial vertical direction is

$Mg left parenthesis square root of 2 minus 1 right parenthesis$
$Mg left parenthesis square root of 2 plus 1 right parenthesis$
$Mg square root of 2$
$fraction numerator Mg over denominator square root of 2 end fraction$

Solution

Mg left parenthesis square root of 2 minus 1 right parenthesis

straight F calligraphic l space sin space 45 space equals space M g left parenthesis calligraphic l minus calligraphic l space cos space 45 right parenthesis F space equals space M g left parenthesis square root of 2 minus 1 right parenthesis

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