Question

A hollow sphere rolls down a ${30}^0$ incline of length 6m without slipping. The speed of centre of mass at the bottom of plane is

• A. $6m{s}^{-1}$
• B. $3m{s}^{-1}$
• C. $6\sqrt{2}m{s}^{-1}$
• D. $3\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is A $6m{s}^{-1}$

Since the sphere rolls down without slipping, it is performing pure rolling motion

Hence $v=Rw$

Applying conservation of energy (Let the mass of sphere be m)

Ei=mgh(h=6sin30 the height of top of incline from ground)

$Ei=m10\left(6sin30\right)$

$Ei=30m$

$Ef=1/2mv2+1/2Iw2$ ( I is the moment of inertia I=2/3 MR2 for hollow sphere)

$Ef=1/2mR2w2+1/2\left(2/3mR2\right)w2$

$Ef=5/6mR2w2$

Solving Ei=Ef you will have

$R2w2=36$

$Rw=6=vcm$

$=6m{s}^{-1}$