If a planet existed whose mass and radius wer | vedclass

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

Question

(D) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constan

Vedclass · Accepted Answer

$19.6$

Vedclass · Answer

(D) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.For Earth,$g_e = \frac{GM_e}{R_e^2} = 9.8 \, m s^{-2}$.For the new planet,the mass $M_p = \frac{M_e}{2}$ and the radius $R_p = \frac{R_e}{2}$.Substituting these values into the formula for the new planet's gravity $g_p$:$g_p = \frac{G(M_e/2)}{(R_e/2)^2} = \frac{G M_e / 2}{R_e^2 / 4} = 2 	imes \frac{GM_e}{R_e^2}$.Since $\frac{GM_e}{R_e^2} = g_e$,we have $g_p = 2 	imes g_e$.$g_p = 2 	imes 9.8 \, m s^{-2} = 19.6 \, m s^{-2}$.

If a planet existed whose mass and radius were both half that of the Earth,the acceleration due to gravity at its surface would be: (in $, m s^{-2}$)

Similar Questions

$A$ ball is thrown vertically upward,acceleration due to gravity is:

Gravitational force on an imaginary planet is six times stronger than the gravitational force of the Earth. Determine the value of acceleration due to gravity and the weight of an object of mass $50 \, kg$ on that planet.

$A$ stone is dropped from a height of $20\, m$.
$(a)$ How long will it take to reach the ground?
$(b)$ What will be its speed when it hits the ground? $(g=10\, m s^{-2})$

What is the source of centripetal force that a planet requires to revolve around the Sun? On what factors does that force depend?

On Earth,how much force is needed to lift an object of mass $100 \,g$ (in $,N$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module