Question

A mass is supported on a frictionless surface. It is attached to a string and rotates about a fixed center at an angular velocity ${\Omega }_0$. If the length of the string and angular velocity are double the tension in the string which was initially $T_0$ is.

• A. $T_0$
• B. $T_0/2$
• C. $4T_0$
• D. $8T_0$

Answer 1

The correct option is D $8T_0$

We know that,

$T=m{\Omega }_o^{2}l$

Where T is the tension, ${\Omega }_o$ is the angular velocity, m is the mass and l is the length.

Now,

$\frac{T_2}{T_1}=\frac{{\Omega }_2^2}{{\Omega }_1^2}\times \frac{l_2}{l_1}$

$\Rightarrow \frac{T_2}{T_o}=\frac{(2\Omega {)}^2}{\Omega }\times \frac{2l}{l}$

$\Rightarrow T_2=8T_o$