The kinetic energy needed to project a body of mass m from the earth's surface (radius R ) to infinity is :

Question

The kinetic energy needed to project a body of mass m from the earth's surface (radius R ) to infinity is : (A) (m g R/2) (B) 2 mgR (C) m g R (D) (m g R/4)

Tardigrade Admin · Accepted Answer

The minimum kinetic energy required to project a body of mass m from earth's surface to infinity is known as escape energy. Therefore, KE =(G Me m/R)=m g R (∵ g R=(G Me/R))

Q. The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$ ) to infinity is :

$\frac{m g R}{2}$

$2 m g R$

$m g R$

$\frac{m g R}{4}$

The minimum kinetic energy required to project a body of mass $m$ from earth's surface to infinity is known as escape energy. Therefore,
$K E = \frac{G M _{e} m}{R} = m g R$
$(∵ g R = \frac{G M _{e}}{R})$

Q. The kinetic energy needed to project a body of mass m from the earth's surface (radius R ) to infinity is :

2mgR​

2mgR

mgR

4mgR​