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

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:

With what velocity should a particle be projected so that its height becomes equal to the radius of the Earth?

Under the influence of a central force,which of the following is conserved?

If the gravitational acceleration at the surface of the Earth is $g$,then the increase in potential energy in lifting an object of mass $m$ to a height equal to half of the radius of the Earth from the surface will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module