Question

Two small spheres each of mass $m$ connected by a string of length $2l$ are kept on a smooth horizontal surface. A vertical force F is applied at the middle of the string. What is maximum value of F for which the spheres do not lose contact with the surface?

• A. $2\, mg$
• B. $mg$
• C. $\frac{3\,mg}{2}$
• D. $4\,mg$

Answer 1

Answer: (A)

$F=2T\,sin\,\theta \ldots(i)$
$T\,sin\,\theta+N =mg$
$N=mg-T\,sin\,\theta \ldots(ii)$

For no loss of contact:
$N >\,0$
$\Rightarrow mg-T\,sin\,\theta>\,0$
$\Rightarrow mg-\frac{F}{2}>\,0$
$\Rightarrow F <\,2\,mg$
So $F_{\text{max}} =2\,mg$