Verified Solution • 2025–26 Session moderate

QJEEM22Ph014c: JEE Main 2022 Physics - Class 11 JEEM22Ph014c Solution: A solid cylinder and a solid sphere, having same mass and…

A solid cylinder and a solid sphere, having same mass MM and radius RR , roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

Multiple Choice Options

  • A 53\sqrt{\frac{5}{3}}
  • B 45\sqrt{\frac{4}{5}}
  • C 35\sqrt{\frac{3}{5}}
  • D 1415\sqrt{\frac{14}{15}}

Step-by-Step Verified Solution

a=gsin⁡θ1+K2R2a = {{g\sin \theta } \over {1 + {{{K^2}} \over {{R^2}}}}}

v=2Sgsin⁡θ1+K2R2v = \sqrt {{{2Sg\sin \theta } \over {1 + {{{K^2}} \over {{R^2}}}}}}

⇒vcvss1+Kss2R21+Kc2R2=1+251+12\Rightarrow {{{v_c}} \over {{v_{ss}}}}\sqrt {{{1 + {{K_{ss}^2} \over {{R^2}}}} \over {1 + {{K_c^2} \over {{R^2}}}}}} = \sqrt {{{1 + {2 \over 5}} \over {1 + {1 \over 2}}}}

⇒7532=1415\Rightarrow \sqrt {{{{7 \over 5}} \over {{3 \over 2}}}} = \sqrt {{{14} \over {15}}}

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