A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all…

Question

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights

h_{s p h}

and

h_{c y l}

on the inline. The ratio

\frac{h_{s p h}}{h_{c y l}}

is given by:

MARKS Content Team · Accepted Answer

Correct answer: (C) 14/15. From conservation of mechanical energy, For solid sphere: 1/2m_sphV^2+1/2I_sphω^2=m_sphgh_sph (V^2)/2+(V^2)/5=gh_sph (7V^2)/10=gh_sph …(i) For cylinder: 1/2m_cylV^2+1/2I_cylω^2=m_cylgh_cyl (V^2)/2+(V^2)/4=gh_cyl (3V^2)/4=gh_cyl …(ii) From (i) and (ii) h_sph/h_cyl=14/15

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{s p h}$ and $h_{c y l}$ on the inline. The ratio $\frac{h_{s p h}}{h_{c y l}}$ is given by:

Solution

Relevant Questions

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph and hcyl on the inline. The ratio hsphhcyl is given by:

Solution

Relevant Questions

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{s p h}$ and $h_{c y l}$ on the inline. The ratio $\frac{h_{s p h}}{h_{c y l}}$ is given by: