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A::B::CSolution :

Considering the motion of the platform <br> `x=A cos omegat`<br> `rArr (dx)/(dt) =- A omega sin omegat rArr(d^2x)/(dt^2) =- A omega^2 con omegat` <br> The magnitude of the maximum acceleration of the platform is <br> `:. |Max acceleration| = A omega^2` <br> When platform moves a torque acts on the cylinder and the <br> cylinder rotates about its exis. <br> Acceleration of cylinder, `a_1 = (f)/(m)` <br> Torque `pi = fR :. l alpha = fR` <br> `alpha = (fR)/(I) = (fr)/(MR^2 /2)` <br> or, `alpha = (2f)/(MR) or Ralpha = (2f)/(M)` <br> `:. Equivalent linear acceleration (Ralpha = a_2)` <br> `a_2 = (2f)/(M)` <br> :. Total linear acceleration, <br> `a_(max) = a_1 +a_2 = (f)/(M)+(2f)/(M) = (3f)/(M)`<br> or,`Aomega^2 = (3f)/(M) or , f = (MAomega^2)/(3)` <br> Thus, maximum torque, <br> `tau_(max) = fxxR = (MAomega^2R)/(3) = (1)/(3) MARomega^2`**Basic Property Of Rigid Body**

**Rigid Body Motion**

**Velocity And Acceleration Of A Point In Rotating Rigid Body In Pure Rotation**

**Relative Angular Velocity In Case Of A Rigid Body**

**Rotational And Translationa Motion Together**

**Rolling Motion**

**Moment Of Inertia Of Rigid Body**

**Uniform Rectangular Sheet**

**Triangular Lamina About Its Base**

**INERTIA OF SQUARE SHEET ABOUT IT'S DIAGONAL**