The angular speed of a body changes from ω1 to ω2 without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is

Question

The angular speed of a body changes from ω1 to ω2 without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is (A) √ω1:√ω2 (B) √ω2:√ω1 (C) ω2:ω1 (D) ω1:ω2

Tardigrade Admin · Accepted Answer

In the absence of external torque I1 ω1=I2 ω2 or MK21 ω1=MK22 ω2 =(K1/K2)=√(ω2/ω1)

Q. The angular speed of a body changes from $ω_{1}$ to $ω_{2}$ without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is

$ω_{1} : ω_{2}$

$ω_{2} : ω_{1}$

$ω_{2} : ω_{1}$

$ω_{1} : ω_{2}$

In the absence of external torque
$I_{1} ω_{1} = I_{2} ω_{2}$
or $M K_{1}^{2} ω_{1} = M K_{2}^{2} ω_{2}$
$= \frac{K _{1}}{K _{2}} = \frac{ω _{2}}{ω _{1}}$

Q. The angular speed of a body changes from ω1​ to ω2​ without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is

ω1​​:ω2​​

ω2​​:ω1​​

ω2​:ω1​

ω1​:ω2​

In the absence of external torque I1​ω1​=I2​ω2​ or MK12​ω1​=MK22​ω2​ =K2​K1​​=ω1​ω2​​​

Q. The angular speed of a body changes from $ω_{1}$ to $ω_{2}$ without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is

$ω_{1} : ω_{2}$

$ω_{2} : ω_{1}$

$ω_{2} : ω_{1}$

$ω_{1} : ω_{2}$

In the absence of external torque
$I_{1} ω_{1} = I_{2} ω_{2}$
or $M K_{1}^{2} ω_{1} = M K_{2}^{2} ω_{2}$
$= \frac{K _{1}}{K _{2}} = \frac{ω _{2}}{ω _{1}}$