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JEE Main 2014 (9 Apr, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2014 (9 Apr, Shift 1)

Q77JEE Main 2014 · 9 APR · SHIFT 1Medium

Rolling Motion

A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio sin⁡θcsin⁡θs\frac{\sin\theta_c}{\sin\theta_s} is:

Figure

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Answer: (d)

  1. Cylinder: ac=23gsin⁡θca_c = \frac{2}{3}g\sin\theta_c; sphere: as=57gsin⁡θsa_s = \frac{5}{7}g\sin\theta_s.
  2. Equal accelerations: 23sin⁡θc=57sin⁡θs\frac{2}{3}\sin\theta_c = \frac{5}{7}\sin\theta_s.
  3. sin⁡θcsin⁡θs=5/72/3=1514\dfrac{\sin\theta_c}{\sin\theta_s} = \dfrac{5/7}{2/3} = \dfrac{15}{14}
  4. So the answer is (d).
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