Question

A string can sustain a maximum force of $200\text{N}$ without breaking. A block of mass of $1\text{kg}$ is tied to one end of the string of $2\text{m}$ long and the mass is rotated in a horizontal circular path. The maximum linear speed of mass is (in $\text{m/s}$).

• A. $20\text{m/s}$
• B. $10\text{m/s}$
• C. $30\text{m/s}$
• D. $5\text{m/s}$

Answer 1

The correct option is A $20\text{m/s}$

Given, the mass of block $\left(m\right)=1\text{kg}$
Length of string $\left(l\right)=2\text{m}$
$T_{\text{max}}=200\text{N}$

As we know that, tension provides necessary centripetal force.

$T_{\text{max}}=\frac{m{v}_{\text{max}}^2}{l}$

$\Rightarrow v_{\text{max}}^2=\frac{T_{\text{max}}\times l}{m}$

$v_{\text{max}}=\sqrt{\frac{T_{\text{max}}\times l}{m}}=\sqrt{\frac{200\times 2}{1}}=\sqrt{400}=20\text{m/s}$

Hence option A is the correct answer