Q 49 Calculate the ratio of the times taken by a uniform solid sphere and a disc of the - Physics - Communication Systems

Question

Q 49 Calculate the ratio of the times taken by a uniform solid
sphere and a disc of the same mass and the same diameter to roll
down through the same distance from rest on a smooth inclined
plane
(1) 15 : 14
(2) 15   :   14
(3) 15 2   :   14 2
(4) 14   :   15

Anshu Agrawal · Accepted Answer

Dear student,

For any of the object rolling down the inclined plane,a=gsinθ/(R2 +K2)This means max K or radius of gyration will have minimum accelerationS=ut+12at2here u=0S=12at2t=2SaSo, t1t2=a2a1Here a2 for disc is 23gsinθ and a1 for sphere is 57gsinθ             =23gsinθ57gsinθt1t2=1415
so option 4 is correct

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Q.49. Calculate the ratio of the times taken by a uniform solid sphere and a disc of the same mass and the same diameter to roll down through the same distance from rest on a smooth inclined plane. (1) 15 : 14 (2) 15 : 14 (3) 15 2 : 14 2 (4) 14 : 15

Q.49. Calculate the ratio of the times taken by a uniform solid sphere and a disc of the same mass and the same diameter to roll down through the same distance from rest on a smooth inclined plane.
(1) 15 : 14
(2) $\sqrt{15} : \sqrt{14}$
(3) $15^{2} : 14^{2}$
(4) $\sqrt{14} : \sqrt{15}$