A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the ripe stretched, covers 66 m and traces 120° at the centre, then find the length of the rope.
1). 30 m
2). 45 m
3). 31.5 m
4). 60 m
Let the length of the rope be 'r'
The path is circular, and as the distance covered while tracing a complete 360o is 2πr, which is the circular path's circumference, the distance covered while tracing an angle of 120o will be
(2πr/360o)×120o
=2πr/3
In the problem this distance is given to be 66m
Therefore, 2πr/3=66
⇒r=66×3/2π
=(66×3×7)/(22×2).................using (π=22/7)
=63/2
=31.5m
Therefore the length of the rope is 31.5m.