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Rotational Motion question

2018 · Q143
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Rotational Motion question

2018 · Q143

NEETPhysicsRotational MotionMCQ+4 / −1
A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is
  1. A
    7 : 10
  2. B
    5 : 7
  3. C
    10 : 7
  4. D
    2 : 5
View written solutionFree

Correct answer: B

In rolling motion,

Translational kinetic energy, Kt = 12mv2{1 \over 2}m{v^2}21​mv2

Rotational kinetic energy, Kr = 12Iω2{1 \over 2}I{\omega ^2}21​Iω2

∴\therefore∴ Kt + Kr = 12mv2{1 \over 2}m{v^2}21​mv2 + 12Iω2{1 \over 2}I{\omega ^2}21​Iω2

= 12mv2+12(25mr2)(vr)2{1 \over 2}m{v^2} + {1 \over 2}\left( {{2 \over 5}m{r^2}} \right){\left( {{v \over r}} \right)^2}21​mv2+21​(52​mr2)(rv​)2

= 710mv2{7 \over {10}}m{v^2}107​mv2

∴\therefore∴ KtKt+Kr=12mv2710mv2{{{K_t}} \over {{K_t} + {K_r}}} = {{{1 \over 2}m{v^2}} \over {{7 \over {10}}m{v^2}}}Kt​+Kr​Kt​​=107​mv221​mv2​ = 57{5 \over 7}75​

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