A body of mass m is thrown vertically upward | vedclass

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

Question

(D) According to the law of conservation of energy,the total energy at the surface of the Earth is equal to the total energy at infinity (or a very la

Vedclass · Accepted Answer

$\sqrt{2} v_e$

Vedclass · Answer

(D) According to the law of conservation of energy,the total energy at the surface of the Earth is equal to the total energy at infinity (or a very large distance where the potential energy is zero).Total energy at the surface: $E_i = K_i + U_i = \frac{1}{2} m(\sqrt{3} v_e)^2 - \frac{GMm}{R}$.We know that the escape velocity $v_e = \sqrt{\frac{2GM}{R}}$,so $v_e^2 = \frac{2GM}{R}$,which implies $\frac{GM}{R} = \frac{v_e^2}{2}$.Substituting this into the energy equation: $E_i = \frac{1}{2} m(3 v_e^2) - m(\frac{v_e^2}{2}) = \frac{3}{2} m v_e^2 - \frac{1}{2} m v_e^2 = m v_e^2$.At a very large distance,the potential energy is $0$,so the final energy is $E_f = \frac{1}{2} m v^2$.Equating $E_i = E_f$: $m v_e^2 = \frac{1}{2} m v^2$.$v^2 = 2 v_e^2 \implies v = \sqrt{2} v_e$.

$A$ body of mass $m$ is thrown vertically upward with speed $\sqrt{3} v_e$,where $v_e$ is the escape velocity of a body from the Earth's surface. The final velocity of the body is

Similar Questions

The mass of the moon is $1/144$ times the mass of a planet and its diameter is $1/16$ times the diameter of a planet. If the escape velocity on the planet is $v$,the escape velocity on the moon will be:

Explain escape energy and provide its definition. Also, explain escape speed.

If an object is projected vertically upwards with a speed equal to half the escape speed of Earth,then the maximum height attained by it is ($R$ is the radius of Earth).

The escape velocity for a body projected vertically upwards from the surface of earth is $11.2 \ km/s$. If the body is projected at an angle of $45^o$ with the vertical,the escape velocity will be ......... $km/s$.

Escape velocity at the surface of the Earth is $11.2 \, km/s$. If the radius of a planet is double that of the Earth but its mean density is the same as that of the Earth,then the escape velocity will be ........ $km/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module