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AP EAMCET202123 Aug 2021Evening ShiftPhysicsRotational MotionActual

If rotational inertia parameter of a body rolling down a rough inclined plane (of inclination and height h ) without slipping is given by =I_ C M / M R^2 , then time taken by the body to reach the bottom of the inclined plane is given by

Options

  1. At= 1 (1+ ) 2 h g
  2. Bt= 1 (1+ ) 2 h g
  3. Ct= 1 (1- ) 2 h g
  4. Dt= 1 (1+ ) h g

Correct answer

A. t= 1 (1+ ) 2 h g

Step-by-step solution

Given, mass of body =M Radius =R Angle of inclination = Height of inclined surface =h Also, = I_ CM M R^2 Using, the acceleration produced in body rolling down the inclined plane a= g 1+ I_ CM M R^2 = g 1+ ...(i) By using equation of motion, s=u t+ 1 2 a t^2 where u=0 (initial velocity) t= time taken to reach at bottom. s=0+ 1 2 g (1+ ) t^2 t^2= 2 s(1+ ) g But, from the diagram, h s = s= h Substituting the value of s , we get aligned t & = 2 h(1+ ) g ^2 & = 1 2 h(1+ ) g aligned

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