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  4. A uniform solid sphere of mass m , radius R moving with velocity v0 is rolling without slipping on a frictionless surface. It collides elastically with a frictionless vertical wall. Ratio of magnitude of angular momentum of the sphere before and after the collision about its bottommost point is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-gpglhiwwxkt5.png />

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Q. A uniform solid sphere of mass $m$ , radius $R$ moving with velocity $v_{0}$ is rolling without slipping on a frictionless surface. It collides elastically with a frictionless vertical wall. Ratio of magnitude of angular momentum of the sphere before and after the collision about its bottommost point is

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

$L_{i n}=mv_{0}R+\frac{2}{5}mR^{2}w$
$L_{i n}=\frac{7}{5}mv_{0}R$
$L_{f i n a l}=mv_{0}R-\frac{2}{5}mR^{2}\omega $
$=\frac{3}{5}mvR$
$Ratio=\frac{7}{3}$