An object is propelled vertically to a maximu | vedclass

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

Question

(A) Let $m$ be the mass of the object and $v$ be its speed when it returns to the surface of the planet.At the maximum height,the distance from the ce

Vedclass · Accepted Answer

$2 \sqrt{\frac{2 G M}{5 R}}$

Vedclass · Answer

(A) Let $m$ be the mass of the object and $v$ be its speed when it returns to the surface of the planet.At the maximum height,the distance from the center of the planet is $r_{max} = R + 4R = 5R$. At this point,the velocity of the object is $0$.Using the principle of conservation of mechanical energy between the maximum height and the surface of the planet:$E_{initial} = E_{final}$$U_{max} + K_{max} = U_{surface} + K_{surface}$$-\frac{G M m}{5R} + 0 = -\frac{G M m}{R} + \frac{1}{2} m v^2$$\frac{1}{2} v^2 = \frac{G M}{R} - \frac{G M}{5R}$$\frac{1}{2} v^2 = \frac{G M}{R} (1 - \frac{1}{5}) = \frac{G M}{R} (\frac{4}{5})$$v^2 = \frac{8 G M}{5 R}$$v = \sqrt{\frac{8 G M}{5 R}} = 2 \sqrt{\frac{2 G M}{5 R}}$Thus,the speed of the object when it returns to the surface is $2 \sqrt{\frac{2 G M}{5 R}}$.

An object is propelled vertically to a maximum height of $4 R$ from the surface of a planet of radius $R$ and mass $M$. The speed of the object when it returns to the surface of the planet is

Similar Questions

Write the change in gravitational potential energy of a body lifted at height $h$ from the surface of Earth.

Assuming that the gravitational potential energy of an object at infinity is zero,the change in potential energy (final - initial) of an object of mass $m$,when moved to a height $h$ from the surface of the Earth (of radius $R$),is given by:

An object is projected vertically upward from the earth's surface with a velocity $u = \sqrt{Rg}$,where $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth's surface. Find the maximum height reached by the object.

The change in potential energy,when a body of mass $m$ is raised to a height $nR$ from the earth's surface is ($R =$ Radius of earth)

Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module