A solid rolls down two different inclined planes of the same heights but different angle of inclination. Will it reach the bottoms with the same speed in each case ?

A solid rolls down two different inclined planes of the same heights b

1.	A solid rolls down two different inclined planes of the same heights but different angle of inclination. Will it reach the bottoms with the same speed in each case ?
Answer» SOLUTION :LINEAR KE=`1/2mv^2`ROTATIONAL K.E`=1/2Iomega^2=1/5mv^2` `:. T.E=1/2mv^2+1/5mv^2=7/(10)mv^2`but T.E=mgh `:. Mgh=7/(10)mv^2`i.e `v=sqrt((10)/(7)gh):'vproph` v is the same for both the cases. Yes, the solid sphere will reach the BOTTOM with the same speed both the cases.