Question

A solid sphere rolling on a rough horizontal surface with a linear speed v collides elastically with a fixed, smooth vertical wall. Find the speed of the sphere after it has began pure rolling in the backward direction.

• A.
• B.
• C. $\frac { 4 } { 7 } \mathrm { v }$
• D. None

Answer 1

Answer: (B)

Answer 2

F_fr = Iα =

α = $\frac { 5 \mathrm {~F} _ { \mathrm { r } } } { 2 \mathrm { mr } }$ (just before collision)

after collision

v_f

v- ……….. (i)

-ω + αt= - ω+ $\frac { 5 \mathrm {~F} _ { \mathrm { f } } } { 2 \mathrm { mr } } \mathrm { t }$ .

or rω_f = - rω + t

or v_f = - v + ……….. (ii)

From eq. (i) and (ii)

v_f = - v + $\frac { 5 } { 2 }$ (v – v_f) or v_f = $\frac { 3 } { 7 }$v.