Given below are two statements: one is labell | vedclass

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

Question

(B) The escape velocity $V_{e}$ of a planet is given by the formula $V_{e} = \sqrt{\frac{2GM}{R}}$,where $G$ is the gravitational constant,$M$ is the

Vedclass · Accepted Answer

$A$ is correct but $R$ is not correct.

Vedclass · Answer

(B) The escape velocity $V_{e}$ of a planet is given by the formula $V_{e} = \sqrt{\frac{2GM}{R}}$,where $G$ is the gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.If the escape velocities of two planets $A$ and $B$ are equal,then $\sqrt{\frac{2GM_{1}}{R_{1}}} = \sqrt{\frac{2GM_{2}}{R_{2}}}$.Squaring both sides,we get $\frac{M_{1}}{R_{1}} = \frac{M_{2}}{R_{2}}$,which implies $\frac{M_{1}}{M_{2}} = \frac{R_{1}}{R_{2}}$.This condition allows for different masses $(M_{1} 
eq M_{2})$ as long as their radii are also different in the same proportion. Thus,Assertion $A$ is correct.Reason $R$ states that the product $M_{1}R_{1} = M_{2}R_{2}$ must be the same,which is mathematically incorrect for the given condition. Therefore,$R$ is incorrect.

Similar Questions

The escape velocity of a body projected vertically from the surface of the Earth is $11 \, km/s$. If the body is projected at an angle of $60^\circ$ with the vertical,the escape velocity will be ......... $km/s$.

$A$ rocket is projected in the vertically upwards direction with a velocity $kv_e$,where $v_e$ is the escape velocity and $k < 1$. The distance from the centre of the Earth up to which the rocket will reach is:

If $v_e$ is escape velocity and $v_0$ is orbital velocity of a satellite for an orbit close to the earth's surface,then these are related by:

$Assertion$: The escape speed does not depend on the direction in which the projectile is fired.
$Reason$: Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the Earth rotates about its axis.

Explain escape speed. On what factors does escape velocity not depend?

Vedclass Test Series

Exam Paper Generator

Online Exam Module