A non-uniform rod of length l having mass density λ ( x ) = A + B x 2 is placed on -x-axis with its ends at a , 0 and a + l , 0 . The force it would exert on a point mass m kept at the origin is

Question

A non-uniform rod of length l having mass density λ ( x ) = A + B x 2 is placed on -x-axis with its ends at a , 0 and a + l , 0 . The force it would exert on a point mass m kept at the origin is, G m A l a a + 2 + B l, G m A l a a - l - B l, G m A l a a + l + B l, G m A l a a + l - B l

MARKS App · Accepted Answer

F = ∫ a a + l G m d M x 2 = G m ∫ a a + l ( A + B x 2 ) d x x 2 = G m ∫ a a + l A x 2 d x + ∫ a a + l B d x = G m [ A [ - 1 x ] a a + l + B l ] = G m A 1 a - 1 a + l + B l = G m A l a a + l + B l

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