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Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Motion in a Plane
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Given the following 2 statements, which of the following choices is correct?

Statement-1: One end of a string of length R is tied to stone of mass m and the other end to a small pivot on a frictionless vertical board.The stone is whirled in a vertical circle with the pivot as the centre.The minimum speed the stone must have,when it is at the topmost on the circle,so that the string does not slack is $\sqrt{gR}$

Statement-2: At the topmost point on the circle,the centripetal force is provided partly by tension in the string and partly by the weight of the stone

$\begin{array}{1 1}\text{Statement-1 is true,Statement-2 is true and Statement-2 is the correct explanation for statement-1}\\\text{Statement-1 is true,Statement-2 is true but Statement-2 is NOT the correct explanation for Statement-1}\\\text{Statement-1 is true,Statement-2 is false}\\\text{Statement-1 is false,Statement-2 is true}\end{array} $

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Answer : Statement-1 is true,Statement-2 is true and Statement-2 is the correct explanation for statement-1
When the stone is at the topmost point A on the circle,the centripetal force is provided by (mg+T) as shown in the figure
Thus $\large\frac{mv^2}{R}=$$mg+T$
When the stone is at A,the string will not slack if tension T=0,which gives
$\large\frac{mv^2}{R}$$=mg$
$\Rightarrow v=\sqrt{Rg}$
answered Aug 14, 2014 by sreemathi.v
 

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