question - solid sphere,ring,disc having same mass and radius are placed at the top of an incline and released. the friction coefficient bw the objects and the incline are same but not sufficient to allow pure rolling .least time will be taken by-
a)solid sphere,b)the ring c)the disc d)all will take same time
also the smallest kinetic energy wil be acquired by-
A) ring b)sphere c)disc d)all achieve the same kinetic energy
ans - 1st question - (d) 2nd question-(A) , please explain ????
The time depends only on force exerted on the body.
as to find time we only req. linear acceleration and distance.
and the main force and the frictional force exerted on the bodies are same.
for Energy we have 1/2 mv2 + 1/2 Iw2
so we'll have to see both.
1/2 mv2 is same for all as m and linear v is same.
but let come to 1/2 Iw2
as the frictional force is same on all and the radius is same thrfr,
Angular torque is same, thrfr, angular momentum is same.i.e. Iw is same...
as Iw is same and I for ring > I for disc > I for sphere
thrfr w for ring < w for disc <w for sphere.
and thrfr the K.E.
thank you but why cant we think this way,since all stuff identical work done by frictional force is same ,
Wext= change in kinetic + change in potential enrgy
since work done by friction is same and change in potential energy is same , so change in kinetic energy must be same????? hence all should come down with same k.e????