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A solid sphere, disc and solid cylinder all of same mass and made up of same material are allowed to roll down (from rest) on an inclined plane, then (a) solid sphere reaches the bottom late (b) solid sphere reaches the bottom first (c) disc will reach the bottom first (d) all will reach the bottom at the same time choose and explain please!!!!!!!!

A solid sphere, disc and solid cylinder all of same mass and made up of same material are allowed to roll down (from rest) on an inclined plane, then


(a) solid sphere reaches the bottom late


 (b) solid sphere reaches the bottom first


(c) disc will reach the bottom first


(d) all will reach the bottom at the same time


choose and explain please!!!!!!!!

Grade:12

12 Answers

Vikas TU
14148 Points
7 years ago
                                       solid sphere      disc              solid cylinder
Moment of Inertia (I)                    (2/5)MR2        MR2 /2             MR2 /2
Radious of Gyration (K)                Underoot(2/5)     R/root2           R/root2
Any of them on rolling on inclined plane will have an acceleration,
a = gsin8/R2 + K2
It means maximum radius of gyration having object will have minimum acceleration.
Decrease in acceleration .i.e decrease in velocity and thus kinetic energy.
Now, Solid sphere has lowest value of ''K'' thus it rolls down with maximum speed.
Hence it will reach the bottom first.
And disc and solid sphere will reach at the same time with same speed.
(b) is correct!
Approve! plz!
Saurabh Anand
38 Points
7 years ago

(b) solid sphere will reach first....as the bodies are rolling on inclined plane therefore there acceleration will be

a=‹g sinθ›/‹‹1› + ‹I/mr2 › where I is moment of inertia of the body...and thus whose acc will more will reach first...

Vishal Naidu
16 Points
7 years ago

option d

check for the formla 

Akash Kumar Dutta
98 Points
7 years ago

acc=gsin(o) / 1 + I/MR^2
hence acc is prop to 1/I
hence then compare the acc.

Nishant Chandrashekar
18 Points
7 years ago

Lets assume all the three are rolling from an height H above the ground

From conservation of energy:

mgH=(1/2)mv^2 + (1/2)Iw^2, where v is the velocity at the bottom and w is the angular velocity

put w=(v/R)

we get,

v^2={2mgH}/{m + (I/R^2)}

now in this relation only moment of inertia will be different from shape to shape(if the radius is same)

then substitute the value of moment of inertia and then compare which has the highest velocity.The one with the highest velocity would be the one to reach the bottom the fastest

Ashwin Muralidharan IIT Madras
290 Points
7 years ago

Hi Pratiksha,

See all the bodies would loose the same amount of PE and hence all will also gain the same amount of KE.

KE = 1/2(mv^2) + 1/2(Iw^2); with v = rw (fpr pure rolling)

So v (or you can say w as well), will be more for the body with less I value and will reach the bottom first. (Remeber KE will be the same for all the bodies, so more I less v and less I more v).

In this case it would be solid sphere. Option (B).

Regards,

Ashwin (IIT Madras).

Abhishekh kumar sharma
34 Points
7 years ago

                                        olid sphere              disc              solid cylinder
Moment of Inertia (I)         (2/5)MR2                  MR2 /2             MR2 /2
Radious of Gyration (K)       Underoot(2/5)      R/root2           R/root2
Any of them on rolling on inclined plane will have an acceleration,
a = gsin8/R2 + K2
It means maximum radius of gyration having object will have minimum acceleration.
Decrease in acceleration .i.e decrease in velocity and thus kinetic energy.
Now, Solid sphere has lowest value of ''''K'''' thus it rolls down with maximum speed.
Hence it will reach the bottom first.
And disc and solid sphere will reach at the same time with same speed.
(b) is correct!
Approve! plz!
irshad
13 Points
3 years ago
Disc:. disc moment of inertia is 1/2mr2 and have less radius of gyration which means more linear velocity and which means more speed and more speed means it reches first Hoop:. hoop moment of inertia is mr2 which means more radius of gyration which means less linear velocity which shows its less speed so it reaches down late
Deepakkumar Mahour
12 Points
3 years ago
The value of k(square)/r(square) for a given body is minimum which is reach the bottom first. As value of solid sphere is 2/5=0.4 which is minimum so elreach first
Aditya tiwari
14 Points
2 years ago
(2)
here,
V is inversly propirtional to value of k and solid sphere have lowest value of k 
hence it will reach bootom first.
Devang pagare
13 Points
2 years ago
Disc will reach to the bottom first 
Because. Moment of inertia of the disc is highest 
So time taken by the body is directly proportional to the moment of inertia as per. The eq. Below
T=,√2l(1+c)/√gsin°
Where l is length of plane 
             C=moment of inertia 
Rishi Sharma
askIITians Faculty 646 Points
9 months ago
Dear Student,
Please find below the solution to your problem.

See all the bodies would loose the same amount of PE and hence all will also gain the same amount of KE.

KE = 1/2(mv^2) + 1/2(Iw^2); with v = rw (fpr pure rolling)

So v (or you can say w as well), will be more for the body with less I value and will reach the bottom first. (Remeber KE will be the same for all the bodies, so more I less v and less I more v).

Thanks and Regards

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