A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant `K=(4mg)/R` where 2R is the natural length of the spring. The other end spring is fixed to the ground at a horizontal distance 2R from the base of the rod. the mass is released at a height of 1.5 R from ground. A. work done by the spring will be `(mgR)/2`B. work done by the spring will be `9 mgR`C. the velocity of the ring when it reaches the ground will be `sqrt(gR)`D. the velocity of the ring when it reaches the ground will be `2sqrt(gR)`

A ring of mass m can slide over a smooth vertical rod. The ring is con

1.	A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant `K=(4mg)/R` where 2R is the natural length of the spring. The other end spring is fixed to the ground at a horizontal distance 2R from the base of the rod. the mass is released at a height of 1.5 R from ground. A. work done by the spring will be `(mgR)/2`B. work done by the spring will be `9 mgR`C. the velocity of the ring when it reaches the ground will be `sqrt(gR)`D. the velocity of the ring when it reaches the ground will be `2sqrt(gR)`
Answer» Correct Answer - D `W_("Spring")=1/2 kx^(2)` `=1/2xx(4 mg)/R[sqrt(4R^(2)+(9R^(2))/4)-2R]^(2)` `=(mgR)/2` `W_("all forces")=DeltaKE` `(mgR)/2+mg.(3R)/2=1/2 mv^(2)` `V=2sqrt(gR)`

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