Given the following, what is the tension in the string when the nearest mass is a distance of 686 km from the Black hole?
#G=6.673×10^-11 m^3kg-1s-2#

Question

Two masses of 1 kg each are connected by a light, inextensible string of one metre in length. The two masses are now made to approach a Black Hole of mass #8.18×10^30 kg# such that the string connecting them lies along a radius.

Joseph Allen · Accepted Answer

#3380" N"#. Don't try this at home: you might get torn apart (see the explanation).

Let A and B be the masses, where A is closer to the black hole O. Then: The tension is determined by the difference in gravitational force between the two masses. #F_{OA}={GM_OM_A}/{r_{OA}^2}# #F_{OB}={GM_OM_B}/{r_{OB}^2}# As the A and B masses are equal we substitute #M_A# for #M_B# and subtract to get the tension: #T=F_{OA}-F_{OB}=# #GM_OM_A(1/{r_{OA}^2}-1/{r_{OB}^2})# Enter the numbers now and compute: #G=6.67xx10^{-11}" Nm"^2/"kg"^2# (same units in SI system as those given) #M_A(=M_B)=1" kg"#, taken as exact values #r_A=686,000-0.5=685,999.5" m"# #r_B=686,000+0.5=686,000.5" m"# Next #T=3380" N"#. This is over 170 times the gravity of Earth on the same amount of mass. A similar 100-g+ force acting on your mass would pull you apart, even though you are still relatively far from the hole's horizon.

Declan Carroll · Answer

undefined The formula for tension in the string would depend on the gravitational forces acting on the masses and the acceleration due to gravity at that distance from the Black hole. Without this information, it is impossible to calculate the tension in the string near the Black hole. Other details about the system, such as the masses involved and their distances from the Black hole, are also necessary.

Given the following, what is the tension in the string when the nearest mass is a distance of 686 km from the Black hole? #G=6.673×10^-11 m^3kg-1s-2#

Two masses of 1 kg each are connected by a light, inextensible string of one metre in length. The two masses are now made to approach a Black Hole of mass #8.18×10^30 kg# such that the string connecting them lies along a radius.