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  • Two discs having masses in the ratio 1: 2 and radil in the ratio 1: 8 roll down without slipping one by one from an inclined plane of height h. The ratio of their linear velocities on reaching the

Two discs having masses in the ratio 1: 2 and radil in the ratio 1: 8 roll down without slipping one by one from an inclined plane of height h. The ratio of their linear velocities on reaching the ground is 

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m_1gh=\frac{1}{2}m_1v_1^2+\frac{1}{2}I\omega^2\\ since\ \omega=\frac{v}{r_1}and \ I=\frac{m_1r_1^2}{2}\\m_1gh=\frac{1}{2}m_1v_1^2+\frac{1}{2}\frac{m_1v_1^2}{2}=\frac{3m_1v_1^2}{4}\\so\ v_1=\sqrt{\frac{4gh}{3}}\\ simillarly\ v_2=\sqrt{\frac{4gh}{3}}\\therefor\ \frac{v_1}{v_2}=\frac{1}{1}

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