A body is projected vertically upwards from t | vedclass

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

Question

(A) According to the law of conservation of mechanical energy,the total energy at the surface is equal to the total energy at the maximum height $h$.A

Vedclass · Accepted Answer

$R/3$

Vedclass · Answer

(A) According to the law of conservation of mechanical energy,the total energy at the surface is equal to the total energy at the maximum height $h$.At the surface: $E_i = K_i + U_i = \frac{1}{2}mv^2 - \frac{GMm}{R}$Given $v = \frac{v_e}{2}$,where $v_e = \sqrt{\frac{2GM}{R}}$. Thus,$v^2 = \frac{v_e^2}{4} = \frac{2GM}{4R} = \frac{GM}{2R}$.$E_i = \frac{1}{2}m(\frac{GM}{2R}) - \frac{GMm}{R} = \frac{GMm}{4R} - \frac{GMm}{R} = -\frac{3GMm}{4R}$.At maximum height $h$,the velocity is zero,so $E_f = K_f + U_f = 0 - \frac{GMm}{R+h}$.Equating $E_i = E_f$: $-\frac{3GMm}{4R} = -\frac{GMm}{R+h}$.$\frac{3}{4R} = \frac{1}{R+h} \implies 3(R+h) = 4R \implies 3R + 3h = 4R \implies 3h = R \implies h = \frac{R}{3}$.

$A$ body is projected vertically upwards from the surface of a planet of radius $R$ with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

Similar Questions

$A$ body is projected vertically upward from the surface of the earth of radius $R$ into space with velocity $n V_e$ (where $n < 1$ and $V_e$ is the escape velocity). The maximum height from the surface of the earth to which the body can reach is

$A$ planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 \ km/s$,the escape velocity from the surface of the planet would be ........ $km/s$.

$A$ particle released at a large distance from a planet reaches the planet only under gravitational attraction and passes through a smooth tunnel through its centre. If $v_e$ is the escape velocity of a body at the planet,then the particle's speed at the centre of the planet is

The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then the ratio of the escape velocities from the planets is

The potential energy of a satellite is $-8 \times 10^9 \ J$. What is its binding energy (escape energy)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module