An object is kept at rest at a distance of 3R | vedclass

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

Question

(A) To ensure the object does not return to Earth,its total mechanical energy at infinity must be at least zero.Let $m$ be the mass of the object.The

Vedclass · Accepted Answer

$\sqrt{\frac{GM}{2R}}$

Vedclass · Answer

(A) To ensure the object does not return to Earth,its total mechanical energy at infinity must be at least zero.Let $m$ be the mass of the object.The distance of the object from the center of the Earth is $r = R + 3R = 4R$.The potential energy at this point is $U = -\frac{GMm}{4R}$.Let $v$ be the projection speed. The kinetic energy is $K = \frac{1}{2}mv^2$.By the law of conservation of energy:$K_i + U_i = K_f + U_f$$\frac{1}{2}mv^2 - \frac{GMm}{4R} = 0 + 0$$\frac{1}{2}mv^2 = \frac{GMm}{4R}$$v^2 = \frac{GM}{2R}$$v = \sqrt{\frac{GM}{2R}}$

An object is kept at rest at a distance of $3R$ above the earth's surface,where $R$ is the earth's radius. The minimum speed with which it must be projected so that it does not return to earth is (Assume $M =$ mass of earth,$G =$ Universal gravitational constant).

Similar Questions

$A$ meteor of mass $m$ having a speed $v$ at infinity reaches the surface of the earth with a speed of (where $v_e$ is the escape speed from the earth's surface).

Escape velocity on a planet is $v_e$. If the radius of the planet remains the same and the mass becomes $4$ times,the escape velocity becomes:

$A$ particle falls towards the Earth from infinity. Its velocity on reaching the Earth would be:

When the speed of a satellite is increased by $x$ percentage,it will escape from its orbit,where the value of $x$ is ....... $\%$

The escape velocity for the earth is $11.2 \ km/s$. The mass of another planet is $100$ times that of the earth and its radius is $4$ times that of the earth. The escape velocity for this planet will be ......... $km/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module