The force of attraction between two bodies at a certain separation is 10 N. What will be the force of attraction between them if the separation between them is reduced to half?
A. 2.5N
B. 5N
C. 20N
D. 40N
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Hint: Obtain the mathematical expression for the force of attraction between two bodies from Newton’s universal law of gravitation. First consider the given condition. Then for the second condition put the value of the first condition to find the required answer.
Complete step by step answer:
The universal law of gravitation gives us the mathematical expression of the force of attraction between two objects of mass m and M separated by a distance R as,
$F=\dfrac{GmM}{{{R}^{2}}}$
Where, G is the universal gravitational constant.
Let the mass of the two bodies are m and M.
Again, let the initial separation between the two bodies are r.
Given, the force of attraction between the two bodies is 10N.
So, we can write that,
$F=\dfrac{GmM}{{{r}^{2}}}=10N$
Now, the separation between the two bodies are reduced to half of the initial separation. So, the final separation between the two bodies will be $\dfrac{r}{2}$ .
Now, the force of attraction between the two bodies will be,
${{F}_{f}}=\dfrac{GmM}{{{\left( \dfrac{r}{2} \right)}^{2}}}=4\dfrac{GmM}{{{r}^{2}}}$
Putting the value from the initial condition on the above equation,
${{F}_{f}}=4\times 10N=40N$
So, the force of attraction between the two bodies when the separation between them is reduced to half will be 40N.
The correct option is (D)
Note:
The force of attraction between two bodies is directly proportional to the product of the mass of the two bodies and inversely proportional to the square of the separation between the two bodies. As the separation between the body decreases, the force of attraction between the two bodies will increase and as the separation between the two bodies increases, the force of attraction between the two bodies will decrease.
Complete step by step answer:
The universal law of gravitation gives us the mathematical expression of the force of attraction between two objects of mass m and M separated by a distance R as,
$F=\dfrac{GmM}{{{R}^{2}}}$
Where, G is the universal gravitational constant.
Let the mass of the two bodies are m and M.
Again, let the initial separation between the two bodies are r.
Given, the force of attraction between the two bodies is 10N.
So, we can write that,
$F=\dfrac{GmM}{{{r}^{2}}}=10N$
Now, the separation between the two bodies are reduced to half of the initial separation. So, the final separation between the two bodies will be $\dfrac{r}{2}$ .
Now, the force of attraction between the two bodies will be,
${{F}_{f}}=\dfrac{GmM}{{{\left( \dfrac{r}{2} \right)}^{2}}}=4\dfrac{GmM}{{{r}^{2}}}$
Putting the value from the initial condition on the above equation,
${{F}_{f}}=4\times 10N=40N$
So, the force of attraction between the two bodies when the separation between them is reduced to half will be 40N.
The correct option is (D)
Note:
The force of attraction between two bodies is directly proportional to the product of the mass of the two bodies and inversely proportional to the square of the separation between the two bodies. As the separation between the body decreases, the force of attraction between the two bodies will increase and as the separation between the two bodies increases, the force of attraction between the two bodies will decrease.