Introduction:
In this scenario, two positive charges Q and q are placed on opposite sides of a grounded sphere. The sphere has a radius of R, and the charges are located at distances R and 4R from the center of the sphere, respectively. We will discuss the behavior of the charges and the resulting electric field.

Charge distribution:
When a grounded sphere is introduced, it means that it is connected to the ground, which is essentially a large reservoir of electrons. This allows the sphere to become electrically neutral as the excess charge is transferred to the ground.

Charge Q:
The charge Q is placed at a distance R from the center of the sphere. Since the sphere is grounded, it will induce opposite charges on its inner surface. The negative charges from the ground will accumulate on the inner surface of the sphere, while positive charges will be repelled to the outer surface. This redistribution of charges will result in a net charge of -Q on the inner surface of the sphere and a net charge of +Q on the outer surface.

Charge q:
The charge q is placed at a distance 4R from the center of the sphere. Similar to the previous case, the grounded sphere will induce opposite charges on its inner and outer surfaces. The inner surface will accumulate a net charge of -q, while the outer surface will have a net charge of +q.

Electric field inside the sphere:
Since the grounded sphere is electrically neutral, the electric field inside the sphere will be zero. This is because the positive charges on the outer surface will cancel out the negative charges on the inner surface, resulting in a net zero electric field.

Electric field outside the sphere:
Outside the sphere, the electric field will not be zero due to the presence of the charges Q and q. The electric field due to charge Q will follow the inverse square law, decreasing with distance from the charge. Similarly, the electric field due to charge q will also follow the inverse square law. The resulting electric field at a point outside the sphere will be the vector sum of the electric fields due to charges Q and q.

Conclusion:
In conclusion, when two positive charges Q and q are placed on opposite sides of a grounded sphere, the sphere will redistribute its charges and become electrically neutral. The electric field inside the sphere will be zero, while outside the sphere, the electric field will be the vector sum of the electric fields due to the charges Q and q.