Question

A string can withstand a tension of $25\text{N}$. What is the greatest speed at which a body of mass $1\text{kg}$ can be whirled in a horizontal circle using a $1\text{m}$ length of a string ?

• A. $2.5{\text{ms}}^{-1}$
• B. $5.0{\text{ms}}^{-1}$
• C. $7.5{\text{ms}}^{-1}$
• D. $10{\text{ms}}^{-1}$

Answer 1

The correct option is B $5.0{\text{ms}}^{-1}$

Since the body is whirled in a horizontal circle, the gravity, acting vertically downwards, has no effect on the motion. If $v$ is the greatest speed with which the body can be whirled, the maximum centripetal force(or tension) in the string is $\frac{m{v}^2}{R}$, which must balance a force of $25\text{N}$. Thus
$25=\frac{m{v}^2}{R}=\frac{1\times v^2}{1}$
which gives $v=5{\text{ms}}^{-1}$, which is choice (b).