Question

A pendulum bob of mass m is suspended by a massless string and at rest when string is vertical. A constant horizontal force F = mg starts acting on it. The value of tension in string is $T=mg[x\sqrt{2}-2]$ when string makes $45°$with the vertical, then the value of $x$ is

• A. 1
• B. 2
• C. 3
• D. 0.0

Answer 1

The correct option is C 3

$T-mgcos\theta -Fsin\theta =\frac{m{V}^2}{l}$
$T-\frac{mg}{\sqrt{2}}-\frac{mg}{\sqrt{2}}=\frac{m{V}^2}{l}...........\left(1\right)Fromwork-energytheorem,\frac{1}{2}m{V}^2=mglsin\theta -mgl(1-cos\theta )\frac{1}{2}m{V}^2=mg\frac{1}{\sqrt{2}}-mgl(1-\frac{1}{\sqrt{2}})=\sqrt{2}mgl-mgl............\left(2\right)Fromequation\left(1\right)and\left(2\right)T=mg\sqrt{2}+2\sqrt{2}mgl-2mg=mg[3\sqrt{2}-2]\therefore x=3$