Show that the velocity of an object released from rest at infinity reaches the earth with a velocity equal to the escape velocity .

Show that the velocity of an object released from rest at infinity rea

1.	Show that the velocity of an object released from rest at infinity reaches the earth with a velocity equal to the escape velocity .
Answer» Solution :By the principle of conservation of energy for the OBJECT , TE at infinity = (KE +PE) at the surface of the earth. As the body is released from rest at infinity , its KE at infinity is zero and its PE at infinity isalso zero. If v is its VELOCITY on reaching the earth its KE BECOMES equal to `1/(2)mv^2 and PE = (GMM)/R` `:. 0 +0 =1/(2)mv^(2) -(GMm)/R` `1/(2)v^(2)=(GM)/R` The velocity of the object, `V = sqrt((2GM)/R) =V_(e)`