Match the following.Column-I (Initially)Column-II (When rolling begins)A) ω=2vRvcm is towards left in case of ring.B) ω=2vRvcm is towards left in case of solid sphere.C) ω=v2Rvcm is towards right in case of ring.D) ω=v2Rvcm is towards right in case of solid sphere.

Taking into the plane –vea) L=MvR+Iω>0⇒v→f leftb) L=MvR−Iω=MvR−I(2vR)MvR−2MvR 0 for solid sphere ⇒v→f leftc) L=MvR+Iω>0⇒v→fd) L=MvR+IωMvR−25MR2(v2R)>0⇒v→f leftMvR−MR2(v2R)>0⇒v→f left

Match the following.Column-I (Initially)Column-II (When rolling begins)A) ω=2vRvcm is towards left in case of ring.B) ω=2vRvcm is towards left in case of solid sphere.C) ω=v2Rvcm is towards right in case of ring.D) ω=v2Rvcm is towards right in case of solid sphere.

Taking into the plane –vea) L=MvR+Iω>0⇒v→f leftb) L=MvR−Iω=MvR−I(2vR)MvR−2MvR 0 for solid sphere ⇒v→f leftc) L=MvR+Iω>0⇒v→fd) L=MvR+IωMvR−25MR2(v2R)>0⇒v→f leftMvR−MR2(v2R)>0⇒v→f left

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Match the following.
Column-I (Initially) Column-II (When rolling begins)
A)
$ω = \frac{2 v}{R}$
$v_{c m}$ is towards left in case of ring.
B)
$ω = \frac{2 v}{R}$
$v_{c m}$ is towards left in case of solid sphere.
C)
$ω = \frac{v}{2 R}$
$v_{c m}$ is towards right in case of ring.
D)
$ω = \frac{v}{2 R}$
$v_{c m}$ is towards right in case of solid sphere.

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A–PR, B–QR, C–PQ, D–QR

A–PS, B–QS, C–PQ, D–PQ

A–PQ, B–QP, C–PR, D–PQ

A–PQ, B–QR, C–PQ, D–PQ

answer is D.

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Detailed Solution

Taking into the plane –ve

$a) L = M v R + I ω > 0 \Rightarrow {\vec{v}}_{f}$ left

$b) L = M v R - I ω = M v R - I (\frac{2 v}{R})$

$M v R - 2 M v R < 0$ for ring $\Rightarrow {\vec{v}}_{f}$ forward

$M v R - \frac{4}{5} M v R > 0$ for solid sphere $\Rightarrow {\vec{v}}_{f}$ left

$c) L = M v R + I ω > 0 \Rightarrow {\vec{v}}_{f}$

$d) L = M v R + I ω$

$M v R - \frac{2}{5} M R^{2} (\frac{v}{2 R}) > 0 \Rightarrow {\vec{v}}_{f}$ left

$M v R - M R^{2} (\frac{v}{2 R}) > 0 \Rightarrow {\vec{v}}_{f}$ left

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Column-I (Initially)	Column-II (When rolling begins)
A) $ω = \frac{2 v}{R}$	$v_{c m}$ is towards left in case of ring.
B) $ω = \frac{2 v}{R}$	$v_{c m}$ is towards left in case of solid sphere.
C) $ω = \frac{v}{2 R}$	$v_{c m}$ is towards right in case of ring.
D) $ω = \frac{v}{2 R}$	$v_{c m}$ is towards right in case of solid sphere.

Match the following.Column-I (Initially)Column-II (When rolling begins)A) ω=2vRvcm is towards left in case of ring.B) ω=2vRvcm is towards left in case of solid sphere.C) ω=v2Rvcm is towards right in case of ring.D) ω=v2Rvcm is towards right in case of solid sphere.

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