The acceleration due to gravity on a planet i | vedclass

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

Question

(D) To ensure safety,the velocity attained upon reaching the ground must be the same on both the Earth and the planet.Let $g_1 = 9.8 \, m/s^2$ be the

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(D) To ensure safety,the velocity attained upon reaching the ground must be the same on both the Earth and the planet.Let $g_1 = 9.8 \, m/s^2$ be the acceleration due to gravity on Earth and $h_1 = 3 \, m$ be the safe height on Earth.Let $g_2 = 1.96 \, m/s^2$ be the acceleration due to gravity on the planet and $h_2$ be the corresponding safe height on the planet.The velocity $v$ attained after falling from height $h$ is given by $v = \sqrt{2gh}$.Equating the velocities for safety: $\sqrt{2 g_1 h_1} = \sqrt{2 g_2 h_2}$.Squaring both sides: $g_1 h_1 = g_2 h_2$.Substituting the values: $9.8 	imes 3 = 1.96 	imes h_2$.$h_2 = \frac{9.8 	imes 3}{1.96} = 5 	imes 3 = 15 \, m$.Thus,the corresponding height on the planet is $15 \, m$.

The acceleration due to gravity on a planet is $1.96 \, m/s^2$. If it is safe to jump from a height of $3 \, m$ on the Earth,the corresponding height on the planet will be ........ $m$.

Similar Questions

If the radius of the earth contracts by $2\%$ and its mass remains the same,then the weight of a body at the earth's surface:

Suppose that the angular velocity of rotation of the earth is increased. Then,as a consequence:

The depth at which acceleration due to gravity becomes $\frac{g}{n}$ is [ $R$ = radius of earth,$g$ = acceleration due to gravity,$n=$ integer].

At what depth below the surface of the earth,will the acceleration due to gravity $g$ be half of its value at $1600 \, km$ above the surface of the earth?

Which graph correctly represents the variation of acceleration due to gravity $(g)$ with radial distance $(r)$ from the centre of the earth (radius of the earth $= R_e$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module