A satellite is revolving around the earth at a height h. The satellite explodes into two equal parts, one part has zero velocity after the explosion, and the other moves in the same direction with double the orbital speed of the original satellite. The maximum height reached by the part with double the velocity is (Neglect the gravitational effects between the fragments)

(A) 3h + 4R              (B) 3R + 4h
(C) 3(R +h)              (D) none of these 


 

Dear student
let initial the satellite has mass M and mass of earth is m , 
initially the satellite is at distance r= h+R (from the centre of earth)and when it reaches the maximum height its distance is r0 from centre of earth hence  r=R+H  (here H is height from surface of earth)
applying angular momentum conservation principle after breaking and when itb reaches its max heightm1 v0r1=m2 v1r2  (here v0and v1 are orbital speed)2M×v0×r =M×v1×r0 v1=2v0rr0....1>now initial total energy after breaking and when it reaches the maximum height  are equalUi +Ki=Uf +Kf-2GMmr+12M(2v0)2= -GMmr0+12M(v1)2now putting the value of v1 from eq 1 we get-2GMmr+12M(2v0)2=-GMmr0+12M2v0rr02-2Gmr+2v02=-Gmr0+2v20r2r02   ....2>now formula of orbital speed  v0=Gmr   and putting in eq 2 and solving avove equation r0 =2r=2R+2hR+H=2R+2hH=R+2h
Regards

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