The ratio of the acceleration due to gravity | vedclass

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

Question

(A) The escape velocity $v_e$ from the surface of a planet is given by the formula $v_e = \sqrt{2 g R}$,where $g$ is the acceleration due to gravity a

Vedclass · Accepted Answer

$\sqrt{K_1 K_2}$

Vedclass · Answer

(A) The escape velocity $v_e$ from the surface of a planet is given by the formula $v_e = \sqrt{2 g R}$,where $g$ is the acceleration due to gravity and $R$ is the radius of the planet.Given the ratio of acceleration due to gravity $\frac{g_1}{g_2} = K_1$ and the ratio of radii $\frac{R_1}{R_2} = K_2$.The ratio of escape velocities is $\frac{v_{e1}}{v_{e2}} = \sqrt{\frac{2 g_1 R_1}{2 g_2 R_2}}$.Substituting the given ratios,we get $\frac{v_{e1}}{v_{e2}} = \sqrt{\frac{g_1}{g_2} \cdot \frac{R_1}{R_2}} = \sqrt{K_1 K_2}$.

The ratio of the acceleration due to gravity on two planets $P_1$ and $P_2$ is $K_1$. The ratio of their respective radii is $K_2$. The ratio of their respective escape velocities is

Similar Questions

$A$ body is projected vertically upwards from the Earth's surface. If the velocity of projection is $\left(\frac{1}{3}\right)$ of the escape velocity,then the height up to which the body rises is $(R = \text{radius of Earth})$

The escape velocity for the Earth is $11 \ km/s$. The escape velocity for a planet having twice the radius and the same density as the Earth is .......... $km/s$.

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 ......... $km/s$.

The ratio of the orbital velocity of a body near the surface of a planet to the escape velocity of a body from the surface of the same planet 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module