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

Answer 1

Answer: (A)

$F=2Tsin\theta \dots (i)$

$Tsin\theta +N=mg$

$N=mg-Tsin\theta \dots (ii)$



For no loss of contact:

$N>0$

$\Rightarrow mg-Tsin\theta >0$

$\Rightarrow mg-\frac{F}{2}>0$

$\Rightarrow F<2mg$

So $F_{\text{max}}=2mg$