Question bank/JEE Main/Physics

Two uniform solid spheres of equal radii R, butmass M and 4M have
a centre to centre separation 6R, as shown in figure. A projectile of
mass m in projected from the surface of thesphere of mass M directly
towards the centre of the second sphere. The minimum speed ofthe
projectile so that it reaches the surface of the second sphere
is[IMAGE]. What is n?

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[IMAGE] The projectile need to reach a point on the line joining the centers
of sphere where net electric force on it is zero.
Let the point N has no net electric field due to spheres.
Therefore, $\frac{GM}{x^{2}} = \frac{G.4M}{{(6R - x)}^{2}}$ x = 2R
Apply conservation of mechanical energy at projectile initial position
and particle at N
E_i = E_f
SUB TOPIC: Conservation of mechanical energy

Source: Grass-G / P-22 Physcis Paper 19 Dec Eng..docx