A body is projected with a velocity equal to 3/4th of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth is R)

v=3ve4=342GMR⇒v2=342GMR2=916×2GMR=9GM8R---(1) TE1=TE2 ⇒KE1+PE1=KE2+PE2 ⇒12mv2-GmMR=0-GmMR+h ⇒12m9GM8R-GmMR=0-GmMR+h ⇒916R-1R=-1R+h ⇒9-1616R=-1R+h ⇒-716R=-1R+h ⇒7R+7h=16R ⇒h=16R-7R7=9R7