A `0.098-kg` block slides down a frictionless track as shown in (Fig. 5.208). . The horizontal distance `x` travelled by the block in moving from `A` to `C` is.A. `(1 + sqrt(3)) m`B. `(1 - sqrt(3)) m`C. `(sqrt(3) + 3)) m`D. g meter

A `0.098-kg` block slides down a frictionless track as shown in (Fig.

1.	A `0.098-kg` block slides down a frictionless track as shown in (Fig. 5.208). . The horizontal distance `x` travelled by the block in moving from `A` to `C` is.A. `(1 + sqrt(3)) m`B. `(1 - sqrt(3)) m`C. `(sqrt(3) + 3)) m`D. g meter
Answer» Correct Answer - C (c) `(1)/(2) mv^2 = mg(3 - 1) = 2 mg` [from conservation of energy] or `v = sqrt(4 g) = 2 sqrt(g)` Vertical component at A is `2 sqrt(g) sin 30^@ = sqrt(g)` Time of flight, `T = (2 v sin theta)/(g) = (2 sqrt(g))/(g) = (2)/(sqrt(g))` Using `S = ut + (1)/(2) at^2`, we get `-1 = sqrt(g) t - (1)/(2) "gt"^2 or (1)/(2) "gt"^2 - sqrt(g) t - 1 = 0` `t = (sqrt(g) +- sqrt(g + 4 xx (1)/(2) g))/(2 xx (g)/(2)) t = (1 +- sqrt(3))/(sqrt(g))` Neglecting negative time, `t = (1 +- sqrt(3))/(sqrt(g))` `x = 2 sqrt(g) cos 30^@ [(1 +- sqrt(3))/(sqrt(g))] or x = (sqrt(3) + 3) m`.

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A `0.098-kg` block slides down a frictionless track as shown in (Fig. 5.208). . The horizontal distance `x` travelled by the block in moving from `A` to `C` is.A. `(1 + sqrt(3)) m`B. `(1 - sqrt(3)) m`C. `(sqrt(3) + 3)) m`D. g meter

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