Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed to about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

Question

Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed to about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation (A) WA > WC > WB (B) WC > WB > WA  (C)  WB > WA > WC  (D) WA > WB > WC

Tardigrade Admin · Accepted Answer

Work done required to bring them rest Δ W = Δ KE Δ W = (1/2)Iω2 Δ W propto I for same ω WA : WB: WC = (2/5) MR2: (1/2) MR2: MR2 = (2/5): (1/2): 1 = 4: 5: 10 ⇒ WC > WB > WA

$W_{A} > W_{C} > W_{B}$

$W_{C} > W_{B} > W_{A}$

$W_{B} > W_{A} > W_{C}$

$W_{A} > W_{B} > W_{C}$

Work done required to bring them rest
$Δ W = Δ K E$
$Δ W = \frac{1}{2} I ω^{2}$
$Δ W \propto I$ for same $ω$
$W_{A} : W_{B} : W_{C} = \frac{2}{5} M R^{2} : \frac{1}{2} M R^{2} : M R^{2}$
$= \frac{2}{5} : \frac{1}{2} : 1$
$= 4 : 5 : 10$
$\Rightarrow W_{C} > W_{B} > W_{A}$

Q. Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed to about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

WA​>WC​>WB​

WC​>WB​>WA​

WB​>WA​>WC​

WA​>WB​>WC​

Work done required to bring them rest ΔW=ΔKE ΔW=21​Iω2 ΔW∝I for same ω WA​:WB​:WC​=52​MR2:21​MR2:MR2 =52​:21​:1 =4:5:10 ⇒WC​>WB​>WA​

$W_{A} > W_{C} > W_{B}$

$W_{C} > W_{B} > W_{A}$

$W_{B} > W_{A} > W_{C}$

$W_{A} > W_{B} > W_{C}$

Work done required to bring them rest
$Δ W = Δ K E$
$Δ W = \frac{1}{2} I ω^{2}$
$Δ W \propto I$ for same $ω$
$W_{A} : W_{B} : W_{C} = \frac{2}{5} M R^{2} : \frac{1}{2} M R^{2} : M R^{2}$
$= \frac{2}{5} : \frac{1}{2} : 1$
$= 4 : 5 : 10$
$\Rightarrow W_{C} > W_{B} > W_{A}$