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
B. `Mg//sqrt2`
C. `Mg (sqrt2 -1)`
D. `Mg (sqrt2 + 1)`

Answer

a

Explanation

As is clear from three forces `Mg` `F` and `T` acting on the mass at `B` are in equilibrium
Applying triangle law of vactore
`(F)/(AB) = (Mg)/(OA)`
`F = mg xx (AB)/(OA) = Mg tan 45^(@) = mg`
.