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  4. A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ,ms -1 goes up an inclined plane which makes an angle of 30° with the horizontal plane, without slipping. How low will the sphere take to return to the starting point A ? <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/facef1e7f47f6266bd9aa3cadd854a9e-.png />

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Q. A sphere of mass $2\,\,kg$ and radius $0.5\,m$ is rolling with an initial speed of $1\ ,ms ^{-1}$ goes up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane, without slipping. How low will the sphere take to return to the starting point $A$ ?
image

JEE MainJEE Main 2021System of Particles and Rotational Motion

Solution:

$a =\frac{ g \sin \theta}{1+\frac{ I }{ mR ^{2}}}=\frac{5}{7} \times \frac{10}{2}=\frac{25}{7}$
$=\frac{2 v_{0}}{a}=\frac{2 \times 1 \times 7}{25}$
$=0.56$