Question

A stone of mass 1kg is tied to the end of a string of 1m length. It is whirled in a vertical circle. If the velocity of the stone at the top is 4m/s. What is the tension in the string (at that instant)?
A. 6N
B. 16N
C. 5N
D. 10N

Answer 1

Hint: Let us draw a convenient diagram, according to the given data when a stone of mass is whirled around in a vertical circle the tension which is acting on the string which can be calculated by using the formula.

Complete step by step answer:
From given data:
Mass of stone =1kg
R=1m
V=\[4m{s^{ - 1}}\]

According to the above diagram, the tension force and the force due to gravity which acts downward direction on the stone. And the centripetal force which balances both the above forces.
Therefore,
$\
  T + mg = \dfrac{{m{v^2}}}{r} \\
  \Rightarrow T = \dfrac{{m{v^2}}}{r} - mg \\
    \\
\ $
Substituting the values
$T = \dfrac{{1 \times {4^2}}}{1} - 1(10)\\
\Rightarrow T=16-10\\
\Rightarrow T=6N\\
$
Hence the correct option is A.

Note: Here we can understand clearly that is when a stone whirled horizontally in a circle which is tied to one end of a string, there is a force exerted inward by the string which is acting on the stone called tension. This tension force in string provides necessary centripetal force for circular motion by stone.