A hallow spere rolls down at ana angle 30 degress incline of lenth 6m without sliping.speed of centre of mass at bottom of plane

Answer 1

Use the conservation of energy 1/2 Iw² + 1/2 Mv²_com =Mgh where h is the height of the ramp which is given by h= 6 sin 30° = 3m I for a hollow sphere is 2/5 MR² using this in the above equation gives 1/2(2/5 MR² w²)

+ 1/2 Mv²_com =Mgh w =v_com /R. So 1/5 MR² v²_com/R² + 1/2 Mv²_com= Mgh. This gives 7 Mv²_com/10= Mgh.

Solving for v_com gives v_com=√10gh/7. Using 9.8m/s²=g v_com=√10*9.8*3 which gives v_com = 17.15 m/s