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 incline. The ratio (hsph/hcyl) is given by :

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 hsph and hcyl on the incline. The ratio (hsph/hcyl) is given by : (A) (14/15) (B) (4/5) (C) 1 (D) (2/√5)

Tardigrade Admin · Accepted Answer

for solid sphere (1/2) mv2 + (1/2) . (2/5) mR2 . (v2/R2) =mghsph for solid cylinder (1/2)mv2 + (1/2) . (1/2) mR2 . (v2/R2) = mghcyl ⇒ (hsph/hcyl) = (7 /5/3 /2) = (14/15)

Q. 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 $h_{cy l}$ on the incline. The ratio $\frac{h _{s p h}}{h _{cy l}}$ is given by :

$\frac{14}{15}$

$\frac{4}{5}$

$1$

$\frac{2}{5}$

Q. 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 incline. The ratio hcyl​hsph​​ is given by :

1514​

54​

1

5​2​

for solid sphere 21​mv2+21​.52​mR2.R2v2​=mghsph​ for solid cylinder 21​mv2+21​.21​mR2.R2v2​=mghcyl​ ⇒hcyl​hsph​​=3/27/5​=1514​

Q. 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 $h_{cy l}$ on the incline. The ratio $\frac{h _{s p h}}{h _{cy l}}$ is given by :

$\frac{14}{15}$

$\frac{4}{5}$

$1$

$\frac{2}{5}$