Laws Of Motion Question 128
Question: Two small spheres each of mass m connected by a string of length $ 2l $ are kept on a smooth horizontal surface. A vertical forceF 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?
Options:
A) $ 2mg $
B) $ mg $
C) $ \frac{3mg}{2} $
D) $ 4mg $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ F=2T\sin \theta $ or $ T\sin \theta =\frac{F}{2} $
$ T\sin \theta +N=mg $
$ \Rightarrow N=mg-T\sin \theta $ For no loss of contact: N>0 $ \Rightarrow mg-T\sin \theta >0 $
$ \Rightarrow mg-\frac{F}{2}>0 $
$ \Rightarrow F<2mg $ So $ {F _{\max }}=2mg $
