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A body is projected from origin with a velocity v0 along +ve x-axis on which a force $–\alpha x^2$ is acting on it. Find the maximum distance from origin up to which the body can go. (x is the position of particle).

(1) $\left({3mv_0^2\over2\alpha}\right)^{1\over3}$

(2) $\left({3mv_0^2\over2\alpha}\right)^{1\over2}$

(3) $\left({2mv_0^2\over3\alpha}\right)^{1\over3}$

(4) $\left({2mv_0^2\over3\alpha}\right)^{1\over2}$

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