1.

A spring of natural length 10 m and spring constant 10 N/m is connected to a ring of mass 0.1 kg, which if free to move on a frictionless horizontal bar as shown in the figure. The ring is pulled away from 'B' towards 'A' at an angle of 53^(@) with vertical, and released. Find the speed of the ring at 'C' ?

Answer»

90 m/s
60 m/s
30 m/s
zero

Solution :Ring gains kinetic energy at the cost of loss in POTENTIAL of the spring.
Between POSITION 'A' and 'B'
`(1)/(2) k (20 - 10)^(2) - (1)/(2) k (20 - 12)^(2)`
`= (1)/(2) mv^(2)`
`RARR 18 k = mv^(2)`
`V_(B) = sqrt((36.K)/(m)) = sqrt((36 xx 10)/(0.1)) = 60 m//s`
and by smmetry : velocity at 'C' will be zero


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