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A uniform cylinder of mass `m` and radius `R` is in equilibrium on an inclined plane by the action of a light spring of stiffness `k`, gravity and reaction force acting on it. If the angle of inclination of the plane is `phi`, then angular frequency of small oscillations of the cylinder is........... A. `2sqrt((k)/(m))`B. `2sqrt((2k)/(m))`C. `2sqrt((2k)/(3m))`D. `sqrt((2k)/(m))` |
Answer» Correct Answer - C Let, `x` be the displacement of centre of mass of cylinder from mean position. `:.` from rolling concept, elongation in spring `=2x` `:.` Restoring torque about point of contact is: `tau_(rest) =- 2R (2kx) =- 4kxR` but `x = R theta rArr tau_(rest) =- 4kR^(2)theta = I alpha` `= (3)/(2)mR^(2).alpha` and `alpha =- omega^(2) theta` : |
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