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 = TE at the surfece of the earth (KE+PE) at infiniy (KE+PE) at the surface of the earth. As the body is RELEASED from rest at infinity, its KE at inifinity is zero and its PE at infinity is also zero. If v is its velocity on reaching the earth its KE becomes equal to `1/2mv^2` and PE=`(GMm)/R` `therefore 0+0=1/2mv^2 -(GMm)/R , 1/2v^2=(Gm)/R rArr` The velocity of the object `V=sqrt((2GM)/R)= V_e` .