The escape velocity of a sphere of mass m is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The escape velocity $v_e$ of an object from the surface of the Earth is the minimum velocity required for the object to escape the Earth's gravita

Vedclass · Accepted Answer

$\sqrt{\frac{2GM_e}{R_e}}$

Vedclass · Answer

(A) The escape velocity $v_e$ of an object from the surface of the Earth is the minimum velocity required for the object to escape the Earth's gravitational field.It is derived by equating the kinetic energy of the object to the magnitude of its gravitational potential energy at the Earth's surface: $\frac{1}{2}mv_e^2 = \frac{GM_em}{R_e}$.Solving for $v_e$,we get $v_e = \sqrt{\frac{2GM_e}{R_e}}$.Note that the mass of the object $m$ cancels out,meaning the escape velocity is independent of the mass of the projectile.

Column-$I$	Column-$II$
$(1)$ Value of escape velocity on the surface of the Earth	$(a)$ $2.38 \, km \, s^{-1}$
$(2)$ Value of escape velocity on the surface of the Moon	$(b)$ $7.92 \, km \, s^{-1}$
	$(c)$ $11.2 \, km \, s^{-1}$

The escape velocity of a sphere of mass $m$ is given by ($G =$ Universal gravitational constant; $M_e =$ Mass of the earth and $R_e =$ Radius of the earth).

Similar Questions

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Value of escape velocity on the surface of the Earth $(a)$ $2.38 \, km \, s^{-1}$

$(2)$ Value of escape velocity on the surface of the Moon $(b)$ $7.92 \, km \, s^{-1}$

$(c)$ $11.2 \, km \, s^{-1}$

$A$ body is projected vertically upward from the surface of the earth of radius $R$ into space with velocity $n V_e$ (where $n < 1$ and $V_e$ is the escape velocity). The maximum height from the surface of the earth to which the body can reach is

The ratio of the acceleration due to gravity on two planets $P_1$ and $P_2$ is $K_1$. The ratio of their respective radii is $K_2$. The ratio of their respective escape velocities is

There is no atmosphere on the moon because

The escape velocity of a body depends upon its mass as:

Vedclass Test Series

Exam Paper Generator

Online Exam Module