0.61 years is the period of rotation of Venus in earth.
Explanation:
This question explores the R-T relationship. As such, Kepler's third law - that the [tex]\mathrm{T}^{2} / \mathrm{R}^{3}[/tex] ratio is the same for all the planets - must be utilized.
[tex]\frac{T_{\text {earth}}^{2}}{R_{\text {earth}}^{3}}=\frac{T_{\text {venus}}^{2}}{R_{\text {venus}}^{3}}[/tex] from given question [tex]\mathrm{R}_{\mathrm{earth}}=1.5 \times 10^{11}[/tex] [tex]\text { Rvenus }=1.08 \times 10^{11} \text { . Tearth }=1[/tex] year substitute the values in the above formula, [tex]\frac{1^{2}}{\left(1.5 \times 10^{11}\right) 3}=\frac{T_{V e n u s}^{2}}{\left(1.08 \times 10^{11} \mathrm{m}\right) 3}[/tex]
[tex]\text { Tvenus }^{2}=\frac{1^{2} \times\left(1.08 \times 10^{11} \mathrm{m}\right)^{3}}{\left(1.5 \times 10^{11}\right)^{3}}\left(1^{2}\right) \times(0.373)=0.373 \text { Tyenus }=\sqrt{0.373}=0.61 \text { years }[/tex]
