Question

A stone of mass 16kg is attached to a string 144m long and it is whirled in a horizontal circle. The maximum tension in the string can withstand is 16N. The maximum velocity of revolution that can be given to the stone without breaking it, is-

A.)2 m/s
B.)24 m/s
C.)12 m/s
D.)4 m/s

Answer 1

Hint: We will acknowledge all the values given to us by the question. Then we will simply apply the formula for tension in terms of mass and centripetal acceleration. As we know that the formula for centripetal acceleration is $\dfrac{{{v^2}}}{r}$, we will substitute this in the equation of tension. Then we will put all the values given in the question to find out the maximum velocity as asked by the question. Refer to the solution below.

Complete step by step answer:
Formula used: $T = m\left( {{a_n}} \right)$, ${a_n} = \dfrac{{{v^2}}}{r}$.

Given-

Mass of the stone = 16kg
Length of the string is = 144m
The maximum tension which the string can withstand is = 16N

Tension in the string will be-

$\Rightarrow T = m\left( {{a_n}} \right)$

Where

T stands for tension.
M stands for mass of the stone.
And ${a_n}$ stands for centripetal acceleration.

$\Rightarrow T = m\dfrac{{{v^2}}}{r} \\\ \\\ \Rightarrow {T_{\max }} = \dfrac{m}{r}{v_{max}}^2 \\\$

The value of maximum tension is given as 16N. The radius of the circle is equal to the length of the string. So-

$\Rightarrow {T_{\max }} = \dfrac{m}{r}{v_{max}}^2 \\\ \\\ \Rightarrow 16 = \dfrac{{16}}{{144}}{v_{max}}^2 \\\ \\\ \Rightarrow {v_{max}}^2 = 144 \\\ \\\ \Rightarrow {v_{max}} = \sqrt {144} \\\ \\\ \Rightarrow {v_{max}} = 12m/s \\\$

Hence, it is clear that option C is the correct option.

Note: Tension is defined as the force of pull exerted by means of a string axially, a rope, a chain or a related one-dimensional continuous object; tension can also be represented as the action-reaction pairs of the forces acting at either end of the components. The opposite of compression may be tension. At the atomic stage, the restorative force will generate what is often called tension, because atoms and molecules are torn apart and obtain energy from a restore force already present. Every end of a chain or rope under such stress will pull the attached item to return the chain to its relaxed length.