A small steel sphere of mass m is tied to a string of length r and is whirled in a horizontal circle with a uniform angular velocity 2 ω The string is suddenly pulled, so that radius of the circle is halved. The new angular velocity will be

Question

A small steel sphere of mass m is tied to a string of length r and is whirled in a horizontal circle with a uniform angular velocity 2 ω The string is suddenly pulled, so that radius of the circle is halved. The new angular velocity will be (A) 2 ω  (B) 4 ω  (C) 6 ω  (D) 8 ω

Tardigrade Admin · Accepted Answer

When no external torque is acting upon a body rotating about an axis, then angular momentum of the body remains constant.

Therefore,

J = I ω =

constant
where

I = m r^{2}

(moment of inertia)

∴ m_{1} r_{1}^{2} ω_{1} = m_{2} r_{2}^{2} ω_{2}

\Rightarrow ω_{2} = \frac{m _{1} r _{1}^{2} ω _{1}}{m _{2} r _{2}^{2}}

Given,

m_{1} = m, r_{1} = r, ω_{1} = 2 ω

m_{2} = m, r_{2} = \frac{r}{2}

∴ ω_{2} = \frac{m r ^{2} ( 2 ω )}{m ( r /2 ) ^{2}} = \frac{m r ^{2}}{m r ^{2}} 8 ω

\Rightarrow ω_{2} = 8 ω

Q. A small steel sphere of mass $m$ is tied to a string of length $r$ and is whirled in a horizontal circle with a uniform angular velocity $2 ω$ The string is suddenly pulled, so that radius of the circle is halved. The new angular velocity will be

2 $ω$

4 $ω$

6 $ω$

8 $ω$

Q. A small steel sphere of mass m is tied to a string of length r and is whirled in a horizontal circle with a uniform angular velocity 2ω The string is suddenly pulled, so that radius of the circle is halved. The new angular velocity will be

2 ω

4 ω

6 ω

8 ω

Q. A small steel sphere of mass $m$ is tied to a string of length $r$ and is whirled in a horizontal circle with a uniform angular velocity $2 ω$ The string is suddenly pulled, so that radius of the circle is halved. The new angular velocity will be

2 $ω$

4 $ω$

6 $ω$

8 $ω$