(A) Given: $I_1 = 4 \ kg \ m^2$,$r_1 = 0.2 \ m$,$I_2 = 20 \ kg \ m^2$,$r_2 = 0.3 \ m$,$\tau_1 = 10 \ Nm$.Since the belt is non-slipping,the linear acc

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(A) Given: $I_1 = 4 \ kg \ m^2$,$r_1 = 0.2 \ m$,$I_2 = 20 \ kg \ m^2$,$r_2 = 0.3 \ m$,$\tau_1 = 10 \ Nm$.Since the belt is non-slipping,the linear acceleration of the rims is the same: $a = \alpha_1 r_1 = \alpha_2 r_2$.For the smaller wheel: $\tau_1 = I_1 \alpha_1 \implies 10 = 4 \alpha_1 \implies \alpha_1 = 2.5 = 5/2 \ rad/s^2$.For the larger wheel: $\alpha_2 = \alpha_1 (r_1 / r_2) = (5/2) \times (0.2 / 0.3) = (5/2) \times (2/3) = 5/3 \ rad/s^2$.The tension $T$ in the belt provides the torque on the larger wheel: $\tau_2 = T r_2$ and $\tau_1 - T r_1 = I_1 \alpha_1$. However,using the relation $\tau_2 = I_2 \alpha_2$ is more direct: $\tau_2 = 20 \times (5/3) = 100/3 \ Nm$.Matching: $a \to 3, b \to 2, c \to 1$.

Class 11 Physics System of Particles and Rotational Motion Mix Example - System of Particles and Rotational Motion

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Two flywheels are connected by a non-slipping belt as shown in the figure. $I_1 = 4 \ kg \ m^2$,$r_1 = 20 \ cm$,$I_2 = 20 \ kg \ m^2$,and $r_2 = 30 \ cm$. $A$ torque of $10 \ Nm$ is applied on the smaller wheel. Match the entries of column $I$ with appropriate entries of column $II$.
Quantities Their numerical values (in $SI$ units)
a. Angular acceleration of smaller wheel $1$. $5/3$
b. Torque on the larger wheel $2$. $100/3$
c. Angular acceleration of larger wheel $3$. $5/2$

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$a-iii, b-ii, c-i$
B
$a-iii, b-i, c-ii$
C
$a-ii, b-i, c-iii$
D
$a-ii, b-iii, c-i$

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System of Particles and Rotational Motion

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Mix Example - System of Particles and Rotational Motion

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$A$ block of mass $m$ is attached to a pulley disc of equal mass $m$ and radius $r$ by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of $5\, m/s$. Its velocity when the string becomes taut will be

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$A$ solid cylinder of mass $2 \ kg$ and radius $0.2 \ m$ is rotating with an angular velocity of $3 \ rad/s$. $A$ particle of mass $0.5 \ kg$ moving with a velocity of $5 \ m/s$ strikes its periphery and sticks to it. The loss in kinetic energy due to the collision is ....... $J$.

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Consider a sphere of mass $m$ and radius $R$ performing pure rolling motion on a rough surface with velocity $v_0$ as shown in the figure. It makes an elastic impact with a smooth wall,moves back,and eventually starts pure rolling again.

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Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ $SI$ unit of torque $(a)$ $m$

$(2)$ $SI$ unit of radius of gyration $(b)$ $N\,m$

$(c)$ $Js^{-2}$

Column-$I$	Column-$II$
$(1)$ $SI$ unit of torque	$(a)$ $m$
$(2)$ $SI$ unit of radius of gyration	$(b)$ $N\,m$
	$(c)$ $Js^{-2}$

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Quantities	Their numerical values (in $SI$ units)
a. Angular acceleration of smaller wheel	$1$. $5/3$
b. Torque on the larger wheel	$2$. $100/3$
c. Angular acceleration of larger wheel	$3$. $5/2$

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$A$ block of mass $m$ is attached to a pulley disc of equal mass $m$ and radius $r$ by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of $5\, m/s$. Its velocity when the string becomes taut will be

$A$ solid cylinder of mass $2 \ kg$ and radius $0.2 \ m$ is rotating with an angular velocity of $3 \ rad/s$. $A$ particle of mass $0.5 \ kg$ moving with a velocity of $5 \ m/s$ strikes its periphery and sticks to it. The loss in kinetic energy due to the collision is ....... $J$.

Consider a sphere of mass $m$ and radius $R$ performing pure rolling motion on a rough surface with velocity $v_0$ as shown in the figure. It makes an elastic impact with a smooth wall,moves back,and eventually starts pure rolling again.

Match Column-$I$ with Column-$II$. Column-$I$ Column-$II$ $(1)$ $SI$ unit of torque $(a)$ $m$ $(2)$ $SI$ unit of radius of gyration $(b)$ $N\,m$ $(c)$ $Js^{-2}$

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Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ $SI$ unit of torque $(a)$ $m$

$(2)$ $SI$ unit of radius of gyration $(b)$ $N\,m$

$(c)$ $Js^{-2}$