91影视

i) Mass of a black hole,$m_b=1脳{10}^{11}\text{鈥刱驳}$

ii) Radius of black hole$r_{bp}=1脳{10}^{鈭�16}\text{鈥刴}$

iii) Radius of Earth,$r_{ep}=6.37脳{10}^6\text{鈥刴}$

iv) Mass of Earth,$m_e=5.98脳{10}^{24}\text{鈥刱驳}$

This problem is based on Newton鈥檚 law of gravitation. According to Newton鈥檚 law of gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. By balancing both forces, we can find the unknown distance between the black hole and the person.

Formula:

Force of gravitation, $F=\frac{G{m}_1{m}_2}{r^2}$ 鈥�(颈)

Using equation (i), Force between Earth & Person can be given as:

$F_{ep}=\frac{G脳m_e脳m_p}{r_{ep}^2}$

Using equation (i), Force between Black hole& Person can be given as:

$F_{bp}=\frac{G脳m_b脳m_p}{r_{bp}^2}$

If these two forces are equal, then

$\begin{array}{c}{F}_{ep}=F_{bp}\\ \frac{G脳m_e脳m_p}{r_{ep}^2}=\frac{G脳m_b脳m_p}{r_{bp}^2}\\ \end{array}$

Hence,

$\begin{array}{c}\frac{r_{bp}^2}{r_{ep}^2}=\frac{m_b}{m_e}\\ \frac{r_{bp}^2}{{\left(6.37脳{10}^6\text{m}\right)}^2}=\frac{1脳{10}^{11}\text{kg}}{5.98脳{10}^{24}\text{kg}}\\ r_{bp}=\sqrt{\left(\frac{{\left(6.37脳{10}^6\text{鈥刴}\right)}^2脳1脳{10}^{11}\text{kg}}{5.98脳{10}^{24}\text{鈥刱驳}}\right)}\\ =0.824\text{m}\\ 鈮�0.8\text{鈥刴}\end{array}$

The distance at which the gravitational pull match that to the Earth鈥檚 is .$0.8\text{鈥刴}$