Calculate'the final speed acquired by the softd cylinder shown in Fig.2.48 when it rolls down and reaches the bottom of the inclined plane' without slipping. Assume that the inclined plane is frictionless.

Calculate'the final speed acquired by the softd cylinder shown in Fig.

1.	Calculate'the final speed acquired by the softd cylinder shown in Fig.2.48 when it rolls down and reaches the bottom of the inclined plane' without slipping. Assume that the inclined plane is frictionless.
Answer» Solution :The cylinder is initially at. rest and lias. potential energy mgh. As it rolls down, it has feotlv rotational. kinetic JL energy and. transl.atibnal. kinetic energy. Let the linear speed !, attained by the cylinder when- it reaches B be V. `mgh = 1/2 I omega^(2) + 1/2 mv^(2)` M.F. of the-solid cylmder.abbut the axis of rotation = I `I = 1/2 MR^(2)`, m is the mass of the cylinder and r is its RADIUS. `w = v/r` `mgh = 1/2 xx (1/2 mr^(2)) v^(2)/r^(2) + 1/2 mv^(2)` `mgh = 1/4 mv^(2) +1/2mv^(2) = 3/4 mv^(2)` `v^(2) = (4gh)/3, v = sqrt(4/3) gh`