Question

Two solid cylinders connected with a short light rod about common axis have radius R and total mass M rest on a horizontal table top connected to a spring of spring constant k as shown. The cylinders are pulled to the left by x and released. There is sufficient friction for the cylinders to roll. Find time period of oscillation.

• A. $2 \pi \sqrt { \frac { M } { k } }$
• B. $2 \pi \sqrt { \frac { M } { 2 k } }$
• C. $2 \pi \sqrt { \frac { 3 M } { 2 k } }$
• D. $2 \pi \sqrt { \frac { M } { 3 k } }$

Answer 1

Answer: (C)

$2 \pi \sqrt { \frac { 3 M } { 2 k } }$

Answer 2

**A=-kx.R

or a= R$\alpha = - \frac { 2 k x } { 3 M }$

or$\omega = \sqrt { \frac { 2 k } { 3 M } }$

or T =$2 \pi \sqrt { \frac { 3 M } { 2 k } }$