Question

The speed of homogeneous solid sphere after rolling down an incline plane of vertical height h as from rest without sliding is​

Answer 1

➠Solution:-

⇨When a solid sphere rolls on inclined plane, then it has both a rotational as well as translational kinetic energy

⇨Total kinetic energy

K = Krot + Ktrans = 1/2 Iω^2 + 1/2 mv^2

⇨For sphere, moment of inertia about its diameter

I = 2/5 mr^2

∴ K = 1/2 [ 2/5 mr^2 ] ω^2 + 1/2 mv^2

• K = 1/5 mr^2 ω^2 + 1/2 mv^2

• K = 1/5 mv^2 + 1/2 mv^2...[as v=rω]

• K = 7/10 mv^2

[ Refer above attachment ]

⇨On reaching sphere at O, it has only kinetic energy

∴ PE = Total KE

mgh = 7/10 mv^2

⇒ v = √10gh/ 7

Hence,The speed of homogeneous solid sphere will be √10/7 gh !