Given below are two statements: One is labeled as Assertion (A) and other is labeler as Reason (R).

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $\rho$ and radius of the drop is r, then

$T=K\sqrt[]{\raisebox{1ex}{$\rho r^3$}\!\left/ \!\raisebox{-1ex}{$S^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$}\right.}$ is dimensionally correct, where K is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

<p><strong>&nbsp;<math><mrow><mi>T</mi><mo>=</mo><mi>k</mi><mroot><mrow><mfrac><mrow><mi>ρ</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow></mrow></mroot></mrow></math></strong></p><p><strong><math><mrow><mrow><mo> [</mo><mrow><mi>T</mi></mrow><mo>]</mo></mrow></mrow></math>&nbsp;<math><mrow><msup><mrow><mrow><mo> [</mo><mrow><mi>M</mi><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow><mo>]</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mrow><mo> [</mo><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mo>]</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mrow><mo> [</mo><mrow><mi>M</mi><mi>L</mi><msup><mrow><mi>T</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><mo>]</mo></mrow></mrow><mrow><mfrac><mrow><mo>−</mo><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></mrow></math></strong></p><p><strong><math><mrow><mrow><mo> [</mo><mrow><mi>T</mi></mrow><mo>]</mo></mrow></mrow></math>&nbsp;<math><mrow><mo>=</mo><mrow><mo> [</mo><mrow><msup><mrow><mi>M</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mfrac bevelled="true"><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>L</mi></mrow><mrow><mfrac bevelled="true"><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>M</mi></mrow><mrow><mo>−</mo><mfrac bevelled="true"><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mfrac bevelled="true"><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mrow><mo>]</mo></mrow></mrow></math></strong></p><p><strong><math><mrow><mo>=</mo><mrow><mo> [</mo><mrow><msup><mrow><mi>M</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow><mo>]</mo></mrow></mrow></math></strong></p>

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