A body is projected vertically from the Earth | vedclass

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

Question

(A) Let the mass of the Earth be $M$ and its radius be $R$. The escape velocity from the Earth's surface is given by $v_e = \sqrt{\frac{2GM}{R}}$.The

Vedclass · Accepted Answer

$R/3$

Vedclass · Answer

(A) Let the mass of the Earth be $M$ and its radius be $R$. The escape velocity from the Earth's surface is given by $v_e = \sqrt{\frac{2GM}{R}}$.The body is projected with velocity $v = \frac{v_e}{2} = \frac{1}{2} \sqrt{\frac{2GM}{R}} = \sqrt{\frac{GM}{2R}}$.Using the law of conservation of energy between the surface of the Earth and the maximum height $h$:Total Energy at surface = Total Energy at maximum height$-\frac{GMm}{R} + \frac{1}{2}mv^2 = -\frac{GMm}{R+h} + 0$Substituting $v^2 = \frac{GM}{2R}$:$-\frac{GMm}{R} + \frac{1}{2}m \left( \frac{GM}{2R} \right) = -\frac{GMm}{R+h}$$-\frac{GMm}{R} + \frac{GMm}{4R} = -\frac{GMm}{R+h}$$-\frac{3GMm}{4R} = -\frac{GMm}{R+h}$$\frac{3}{4R} = \frac{1}{R+h}$$3(R+h) = 4R$$3R + 3h = 4R$$3h = R$$h = R/3$Therefore, the maximum height reached by the body is $R/3$.

$A$ body is projected vertically from the Earth's surface of radius $R$ with a velocity equal to half the escape velocity. The maximum height reached by the body is

Similar Questions

The escape velocity from the moon's surface is less than that on the earth's surface,because:

The escape velocity from the earth is about $11 \, km/s$. The escape velocity from a planet having twice the radius and the same mean density as the earth is ......... $km/s$.

$A$ boy can jump to a height $h$ on the surface of a planet. If the density of the planet is $d$,what should be its radius $R$ so that the boy can escape from the gravitational pull of the planet?

For the moon to cease to remain the earth's satellite,its orbital velocity has to increase by a factor of

$A$ satellite with kinetic energy $E_k$ is revolving around the Earth in a circular orbit. How much more kinetic energy should be given to it so that it may just escape into outer space?

Vedclass Test Series

Exam Paper Generator

Online Exam Module