Question

A $1\text{kg}$ stone at the end of $1\text{m}$ long string is whirled in a vertical circle at a constant speed of $4\text{m/s}$. The tension in the string is $6\text{N}$, when the stone is
(Take $g=10{\text{m/s}}^2$)

• A. At the top of the circle
• B. At the bottom of the circle
• C. Half way down
• D. None of above

Answer 1

The correct option is A At the top of the circle

Let the position of the stone at an instance as shown in figure.


Centrifugal force acting on the stone,
$\frac{m{v}^2}{R}=\frac{1\times 4^2}{1}=16\text{N}$
Weight of the stone, $mg=1\times 10=10\text{N}$
Balancing the forces acting on the stone,
$\Rightarrow T=\text{mg cos}\theta +\frac{m{v}^2}{R}$
$6=10\text{cos}\theta +16$
$\text{cos}\theta =-1$
$\theta ={180}^{\circ }$
At this angle, the stone will be at the top of the circle.