Infinite number of masses each of 3 kg are placed along a straight line at the distances of 1 m , 2 m , 4 m , 8 m , … … from a point 0 on the same line. If G is the universal gravitational constant, then the magnitude of gravitational field intensity at 0 is

Step-by-step solution

Gravitational field, ∑ F = ∑ G m r 2 ⇒ ∑ F = 3 G ∑ 1 r 2 ⇒ ∑ F = 3 G 1 1 2 + 1 2 2 + 1 4 2 + . . . . . . . . . ⇒ ∑ F = 3 G 1 1 - 1 4 ⇒ ∑ F = 3 G 1 3 4 ⇒ ∑ F = 3 G 4 3 ⇒ ∑ F = 4   G