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

Options

A. `Mg(sqrt(2)+1)`
B. Mg
C. `(Mg)/(sqrt(2))`
D. `Mg(sqrt(2)-1)`

Answer

D

Explanation

The work done by force F is converte into potential energy at certain height h ` = ( l - l cos 45^(@))`

W = mgh
`F.d = Mg (-l cos 45^(@))`
`Fl sin 45^(@) = Mg (l- l cos 45^(@))`
` F = Mg (sqrt(2)-1)`