question_answer

If the diameter of the earth becomes half its present value but its average density remains unchanged then how would be the weight of an object on the surface of the earth affected?

Answer:

                Acceleration due to gravity on the surface of the earth \[g=\frac{GM}{{{R}^{2}}}=\frac{G}{{{R}^{2}}}\times \frac{4}{3}\pi {{R}^{3}}\rho =\frac{4}{3}\pi GR\rho \] When the diameter or radius becomes half its present value, \[g'=\frac{4}{3}\pi G\left( \frac{R}{2} \right)\rho =\frac{g}{2}.\] Hence the weight of the object will be halved.