If two bodies of masses M1 and M2(M1 > M2) are connected by alight inextensible string passing over a smooth pulley, the tension in the string, will be given by A. $${\text{T}} = \frac{{{\text{g}}\left( {{{\text{M}}_1} – {{\text{M}}_2}} \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}$$ B. $${\text{T}} = \frac{{{\text{g}}\left( {{{\text{M}}_1} + {{\text{M}}_2}} \right)}}{{{{\text{M}}_1} \times {{\text{M}}_2}}}$$ C. $${\text{T}} = \frac{{{\text{g}}\left( {{{\text{M}}_2} – {{\text{M}}_1}} \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}$$ D. $${\text{T}} = \frac{{{\text{g}}\left( {{{\text{M}}_2} + {{\text{M}}_1}} \right)}}{{{{\text{M}}_2} – {{\text{M}}_1}}}$$

The correct answer is $\boxed{\text{T} = \frac{{\text{g}}\left( {{{\text{M}}_2} – {{\text{M}}_1}} \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}}$.

Consider the following diagram:

[Diagram of two bodies of masses M1 and M2(M1 > M2) are connected by alight inextensible string passing over a smooth pulley.]

The tension in the string is equal to the force exerted by each mass on the string. The force exerted by a mass on a string is equal to the mass times the acceleration of the mass. The acceleration of each mass is equal to the acceleration due to gravity, $g$, minus the acceleration of the pulley. The acceleration of the pulley is zero, since it is a smooth pulley. Therefore, the tension in the string is equal to:

$${\text{T}} = {{\text{M}}_1}g – {{\text{M}}_2}g = \frac{{{\text{g}}\left( {{{\text{M}}_1} – {{\text{M}}_2}} \right)}}{{{{\text{M}}_1} + {{\text{M}}_2}}}$$

Option A is incorrect because it does not take into account the difference in mass between the two bodies. Option B is incorrect because it divides the force by the product of the masses, instead of the sum of the masses. Option C is the correct answer, as it takes into account the difference in mass between the two bodies and divides the force by the sum of the masses. Option D is incorrect because it does not take into account the difference in mass between the two bodies.