$$ \begin{aligned} &\text { Match the column }\\\ &\begin{array}{|l|l|} \hline \text { Column - I } & \text { Column - II } \\ \hline \text { (1) space is isotropic } & \begin{array}{l} \text { (P) conservation of linear } \\ \text { momentum } \end{array} \\ \hline \text { (2) space is homogeneous } & \text { (Q) conservation of energy } \\ \hline \text { (3) Time is homogeneous } & \begin{array}{l} \text { (R) conservation of charge still } \\ \text { not known } \end{array} \\ \hline \text { (4) Time is isotropic } & \begin{array}{l} \text { (S) conservation of } \\ \text { angular momentum } \end{array} \\ \hline \end{array} \end{aligned} $$ (a) \(1-(\mathrm{S}), 2-(\mathrm{P}), 3-(\mathrm{R}), 4-(\mathrm{Q})\) (b) \(1-(\mathrm{S}), 2-(\mathrm{P}), 3-(\mathrm{Q}), 4-(\mathrm{R})\) (c) \(1-(\mathrm{P}), 2-(\mathrm{S}), 3-(\mathrm{R}), 4-(\mathrm{Q})\) (d) \(1-(\mathrm{R}), 2-(\mathrm{Q}), 3-(\mathrm{P}), 4-(\mathrm{S})\)

Step by step solution

01

1. Space is isotropic

Isotropic space means that the properties of space do not depend on the direction. As a result, angular momentum does not change when the direction changes. This isotropy of space corresponds to the conservation of angular momentum. So, (1) matches with (S).

02

2. Space is homogeneous

Homogeneous space means that the properties of space do not depend on the position. Thus, linear momentum will remain conserved since it does not depend on a specific location. So, (2) matches with (P).

03

3. Time is homogeneous

Homogeneous time means that the properties of time do not depend on a specific moment. In this case, the total energy of a system will remain conserved since it does not depend on a specific point in time. So, (3) matches with (Q).

04

4. Time is isotropic

Isotropic time means the properties of time do not depend on the direction of time. This property still hasn't been proven, and it is not widely known regarding its conservation law. So, (4) matches with (R). Based on the matches above, the correct option is: (b) \(1-(\mathrm{S}), 2-(\mathrm{P}), 3-(\mathrm{Q}), 4-(\mathrm{R})\)

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