A particle is moving with uniform speed along the circumference of...

$F ∝ \dfrac{1}{{R}^{3}}$

$\dfrac{K}{{R}^{3}} = m{\omega}^{2}R$

${\omega}^{2} = \dfrac{K}{m} \times \dfrac{1}{{R}^{4}}$

${\left(\dfrac{2\pi}{T}\right)}^{2} = \dfrac{K}{m} \times \dfrac{1}{{R}^{4}}$

${T}^{2} ∝ {R}^{4}$

$T ∝ {R}^{2}$