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The radius R_h and massM_h of a block hole are related by R_h = 2GM_h//c^2, where c is the speed of light. Assume that the gravitational acceleration a_g of an object at a distance r_o = 1.001R_h from the center of a block hole is given by (it is, for large block holes). (a) In terms of M_h increases ? (b) Does a_g" at "r_o increase or decease as M_hincreases ? (b) Does a_g" at " r_o increase or decrease as M_h increase ? (c) What is a_g" at "r_o for a very large black hole whose mass is 1.55 xx 10^12 times the solar mass of 1.99 xx 10^30 kg ? (d) If an astronaut of height 1.66 m is at r_o with her feet down, what is the difference in gravitational acceleration between her head the difference in gravitaional acceleration between her head and feet ? (e) Is the tendency to stretch the astronaut severe ? |
| Answer» Solution :(a) `(3.02 xx 10^43 KG" " m//s^2)M_h,`(b) `a_g` decreases as `M_h` increases, (c ) `a_g = 9.82 m//s^2,` (d) `7.10 xx 10^(-15) m//s^2`, (e ) The minsule RESULT of the previous PART implies that, in this case,any EFFECTS due to the differences of gravitational forces on the body are NEGLIGIBLE. | |