question_answer

A particle of mass 0.2 kg tied at the end of a spring is being rotated along a vertical circle of radius 0.5 m at critical speed of 5 m/s. The tension T in the string at the highest point of its path is

A)  8.04 N          

B)  11.96N

C)  10 N            

D)  1.96N

Correct Answer: A

Solution :

 When a body tied to the end of a string is rotated in a vertical circle, the speed of the body is different at different points of the circular path when body is at highest point A, it is acted upon by two forces weight mg of the body and tension\[{{T}_{A}}\]in the string. \[\therefore \]\[{{T}_{A}}+mg=\]centripetal force\[=\frac{mv_{A}^{2}}{r}\] \[\Rightarrow \] \[{{T}_{A}}=\frac{mv_{A}^{2}}{r}-mg\] Given, \[m=0.2\,kg,r=0.5m,\,{{v}_{A}}=5\,m/s\] \[\therefore \] \[{{T}_{A}}=\frac{0.2\times {{(5)}^{2}}}{0.5}-0.2\times 9.8\] \[{{T}_{A}}=10-1.96\] \[{{T}_{A}}=8.04N\]