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QJEEM21Ph7924: JEE Main 2021 Physics - Class 11 JEEM21Ph7924 Solution: The following bodies, (1) a ring (2) a disc (3) a solid…

The following bodies,

(1) a ring

(2) a disc

(3) a solid cylinder

(4) a solid sphere,

of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ___________. [Mark the body as per their respective numbering given in the question]

JEE Main 2021 (Online) 17th March Morning Shift Physics - Rotational Motion Question 105 English

Step-by-Step Verified Solution

a=gsin⁡θ(1+ImR2)a = {{g\sin \theta } \over {\left( {1 + {I \over {m{R^2}}}} \right)}}

IR = mR2, aR = g sin θ\theta /2

ID = mR22{{m{R^2}} \over 2} , aD = 23{2 \over 3} g sin θ\theta

ISC = mR22{{m{R^2}} \over 2} , aSC = 23{2 \over 3} g sin θ\theta

ISC = 25{2 \over 5} mR2, aSS = 57{5 \over 7} g sin θ\theta

S = ut + 12{1 \over 2} at2,

t = 2Sa\sqrt {{{2S} \over a}}

∴\therefore t ∝\propto 1a{1 \over {\sqrt a }}

solid sphere will take minimum time.

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