Question

In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?

• A. Weight is doubled
• B. Weight is quadrapled
• C. Weight becomes 16 times
• D. Weight remains same

Answer 1

Answer: (C)

Weight becomes 16 times

The weight of an object is directly proportional to the mass of the earth and inversely proportional to the square of the radius of the earth. i.e.,

If the diameter becomes half, the radius of the earth will also become half. So, they have the same relation.

Weight of a body $\propto \frac{M}{R^2}$

Original weight $W_0=mg=mG\frac{M}{R^2}$

When hypothetically $m$ becomes $4m$ and $R$ becomes $\frac{R}{2}$

Then weight becomes $W_n=mG\frac{4M}{{\left(\frac{R}{2}\right)}^2}=\left(16mG\right)\frac{M}{R^2}=16\times W_0$

Therefore, The weight will become 16 times.