Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track (Fig. 6.16). Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given theta_(1)= 30^(@), theta_(2)= 60^(@)" and "h= 10m, what are the speeds and times taken by the two stones?

Two inclined frictionless tracks, one gradual and the other steep meet

1.	Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track (Fig. 6.16). Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given theta_(1)= 30^(@), theta_(2)= 60^(@)" and "h= 10m, what are the speeds and times taken by the two stones?
Answer» Solution :No, the stone on the STEEP plane REACHES the BOTTOM earlier, YES, they reach with the same speed V, [since `mgh= (1"/"2)mv^(2)`] `v_(B)= v_(c )= 14.1 ms^(-1), t_(B)= 2sqrt(2)s, t_(c )= 2sqrt(2)s`.