Question

jumping height on Δερκσεν name of the planet in Latin letters take-off points velocity on earth gravitational acceleration on the planet's surface lifting, upward acceleration (Archimedes) /3 /4 /3 /4 6 /20

Answer 1

The weight of an object is defined by force at which the object is pulled towards the center.

So, to find the weight of sportsmen whose mass is 85 kg. we need to find the acceleration due to gravity of the given planet.

Now,

Given planet's mass=M = 3*10²⁴ kg

radius =r = 5400km= 5400 *10³ m= 5.4 * 10⁶m

$\Gamma$=6.67 * 10^-11 m³/kgs²

acceleration due to gravity is given by

$g=\frac{\Gamma M }{r^{2}}$

$g=\frac{6.67 * 10^{-11} *3*10^{24} }{(5.4*10^{6})^{2}}ms^{-2}$

$g=6.86ms^{-2}$

So, weight of the sportsmen = 85 * 6.86 N = 583N, which is the required solution.

This is when atmosphere weight is not considered.

Since the atmosphere has also some weight the overall force it exerts downwards will also change.

Now, mass of atmosphere displaced by the human = density of atmosphere * volume = 5kg/m³ * 2.3 m³ =11.5 kg

mass of the air that is used by human to counteract some of the atmospheric forces = density of air * volume = 1.4 kg/m³ * 2.3 m³ = 3.22 kg

So, overall mass of the human changes to = mass of human + mass of atmosphere - mass of air = 85 +11.5-3.22 kg =93.28kg

So, overall weight = 93.28 * 6.86 N= 640 N.

If any doubt feel free to comment