Question

On a planet ( whose size is the same as that of earth and mass 4 time to the earth ) the energy needed to lift a 2 kg mass vertically upwards through 2m distance on the planet is

Answer 1

c of potential energy

Answer 2

Given :

Mass of planet is 4 time to the earth .

To Find :

The energy needed to lift a 2 kg mass vertically upwards through 2m distance on the planet .

Solution :

Acceleration due to gravity on earth is given by :

$g=\dfrac{GM_e}{R^2}=9.8\ m/s^2$

We have given that mass of the planet is 4 times the mass of earth .

Therefore , $M_p=4M_e$ .

So , acceleration on the planet is :

$g_p=\dfrac{GM_p}{R^2}\\\\g_p=\dfrac{G(4M_e)}{R^2}\\\\g_p=4g\\\\g_p=4\times 9.8=39.2\ m/s^2$

We know , energy is given by :

$E=mg_hh\\\\E=2\times 2\times 39.2\ J\\\\E=156.8\ J$

Hence , this is the required solution .

Learn More :

Gravitation

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