An object is projected vertically upward from | vedclass

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

Question

(B) Let an object of mass $m$ be projected with an initial velocity $u = \sqrt{Rg}$ from the surface of the earth. Let it reach a maximum height $h$ a

Vedclass · Accepted Answer

$R$

Vedclass · Answer

(B) Let an object of mass $m$ be projected with an initial velocity $u = \sqrt{Rg}$ from the surface of the earth. Let it reach a maximum height $h$ above the surface of the earth.According to the law of conservation of mechanical energy,the total energy at the surface of the earth is equal to the total energy at the maximum height $h$:$K_i + U_i = K_f + U_f$$\frac{1}{2} m u^2 - \frac{GMm}{R} = 0 - \frac{GMm}{R+h}$Given that $u^2 = Rg$ and $g = \frac{GM}{R^2}$,we have $GM = gR^2$. Substituting $u^2 = Rg$ and $GM = gR^2$ into the equation:$\frac{1}{2} m (Rg) - \frac{(gR^2) m}{R} = - \frac{(gR^2) m}{R+h}$$\frac{1}{2} mgR - mgR = - \frac{mgR^2}{R+h}$$-\frac{1}{2} mgR = - \frac{mgR^2}{R+h}$$\frac{1}{2} = \frac{R}{R+h}$$R + h = 2R$$h = R$

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.

Similar Questions

$A$ body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is (where $g$ is acceleration due to gravity at the surface of the earth).

$A$ stationary object is released from a point $P$ at a distance $3R$ from the centre of the moon,which has radius $R$ and mass $M$. Which of the following gives the speed of the object on hitting the moon?

$A$ mass '$m$' on the surface of the Earth is shifted to a height equal to the radius of the Earth. If '$R$' is the radius and '$M$' is the mass of the Earth,then the work done in this process is:

$A$ missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is

$A$ body of mass $m$ is placed on the earth's surface. It is taken from the earth's surface to a height $h = 3R$. The change in gravitational potential energy of the body is

Vedclass Test Series

Exam Paper Generator

Online Exam Module