InterviewSolution
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InterviewSolution
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Two spherical planets P and Q have the same uniform density `rho,` masses `M_p and M_Q` and surface areas A and 4A respectively. A spherical planet R also has uniform density `rho` and its mass is `(M_P + M_Q).` The escape velocities from the plantes P,Q and R are `V_P V_Q and V_R` respectively. ThenA. `V_Q gt V_R gt V_P`B. `V_R gt V_Q gt V_P`C. `V_P/V_P =3`D. `V_P/ V_ Q =(1)/(2)` |
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Answer» Correct Answer - B::D (b,d) Let the mass of P be m. Then `m = rho xx(4)/(3) pir^3 = rhoxx(4)/(3)pi[(A)/(4pi)]^(3//2)` The mass of `Q = rho xx(4)/(3) pi[(4A)/(4pi)]^(3//2) = 8m` `:. The mass of R = 9m` if the radius of P = r Then the radius of Q =2r `[:. r_Q = ((4A)/(4pi))^(3//2) = 2((A)/(4pi))^(3//2)]` and radius of `R = 9^(1//3)_r` `[:.( M_R = M_p + M_Q),(r_R^3 =r^3 + (2r)^3 = 9r^3)]` `Now, v_p = sqrt((2GM_p)/(R_p)) = sqrt((2Gm)/(r )` `v_Q = sqrt(((2G(9m))/(R_Q)) = sqrt((2G(8m))/(2r)) = 2v_p` `v_R = sqrt((2G(9m))/(9^1/3_r)) = 9^1//3_(vp)` |
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