Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1 and ω2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

Question

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1 and ω2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:- (A) (1/4) I (ω1 - ω2)2 (B) I (ω1 - ω2)2 (C) (1/8) I (ω1 - ω2)2 (D) (1/2) I (ω1+ ω2)2

Tardigrade Admin · Accepted Answer

Δ KE =(1/2) (I1 I2/I1+I2)(ω1-ω2)2 =(1/2) (I2/(2 I))(ω1-ω2)2 =(1/4) l(ω1-ω2)2

$\frac{1}{4} I (ω_{1} - ω_{2})^{2}$

$I (ω_{1} - ω_{2})^{2}$

$\frac{1}{8} I (ω_{1} - ω_{2})^{2}$

$\frac{1}{2} I (ω_{1} + ω_{2})^{2}$

$Δ K E = \frac{1}{2} \frac{I _{1} I _{2}}{I _{1} + I _{2}} (ω_{1} - ω_{2})^{2}$
$= \frac{1}{2} \frac{I ^{2}}{( 2 I )} (ω_{1} - ω_{2})^{2}$
$= \frac{1}{4} l (ω_{1} - ω_{2})^{2}$

41​I(ω1​−ω2​)2

I(ω1​−ω2​)2

81​I(ω1​−ω2​)2

21​I(ω1​+ω2​)2

ΔKE=21​I1​+I2​I1​I2​​(ω1​−ω2​)2 =21​(2I)I2​(ω1​−ω2​)2 =41​l(ω1​−ω2​)2

$\frac{1}{4} I (ω_{1} - ω_{2})^{2}$

$I (ω_{1} - ω_{2})^{2}$

$\frac{1}{8} I (ω_{1} - ω_{2})^{2}$

$\frac{1}{2} I (ω_{1} + ω_{2})^{2}$

$Δ K E = \frac{1}{2} \frac{I _{1} I _{2}}{I _{1} + I _{2}} (ω_{1} - ω_{2})^{2}$
$= \frac{1}{2} \frac{I ^{2}}{( 2 I )} (ω_{1} - ω_{2})^{2}$
$= \frac{1}{4} l (ω_{1} - ω_{2})^{2}$