A mass 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 degrees with the initial vertical direction is

 

1) Mg(root of 2 - 1)

2) Mg (root of 2 +1)

3) Mg multiplied by root of 2

4) Mg/ root of 2

suppose when the angle made by string with vertical is ZERO, then lets take potential energy as 0.

now, when it makes an angle of 45 degree, the mass has risen by:

H = L - Lcos45

now, gravitational PE is mgH

now, since the force is horizontal, work done by that force is only along the horizontal diection.

so, W_F = F*d (where d = Lsin45)

equating the gravitaional potential energy and work done by force,

mgL (2 - 1)/2 = F*L/2

=> F = mg (2 - 1)

so, correct option is 1)

 

RATE me if correct...