jee-main 2025 Q1

jee-main · India · session2_02apr_shift2 Dimensional Analysis
Q1. Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.
(1) $T ^ { 2 } = \frac { 4 \pi ^ { 2 } r ^ { 2 } } { G M }$
(2) $T ^ { 2 } = \frac { 4 \pi ^ { 2 } r } { G M ^ { 2 } }$
(3) $T ^ { 2 } = \frac { 4 \pi ^ { 2 } r ^ { 3 } } { G M }$
(4) $T ^ { 2 } = 4 \pi ^ { 2 } r ^ { 3 }$
Q1. Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.\\
(1) $T ^ { 2 } = \frac { 4 \pi ^ { 2 } r ^ { 2 } } { G M }$\\
(2) $T ^ { 2 } = \frac { 4 \pi ^ { 2 } r } { G M ^ { 2 } }$\\
(3) $T ^ { 2 } = \frac { 4 \pi ^ { 2 } r ^ { 3 } } { G M }$\\
(4) $T ^ { 2 } = 4 \pi ^ { 2 } r ^ { 3 }$