Question

escape velocity of particle on earth radius R and mass M is 11.2 km per second what is the escape velocity of other planet with radius R/2 and mass M/4

Answer 1

Hiii
bro your answer is
Escape velocity for an object of mass m for a planet of mass M at radius R is given by:

m*v*v/2 - G*M*m/R = 0 ,  sum of kinetic enery and potential energy is zero.

m cancels out.

v*v = 2*G*M/R in this case R = radius of earth and M is the mass of the Earth.

Since the planet has the same density as Earth, determine the ratio of the volumes. Let Rp be the planet radius and R the Earth's radius

Vp = planet volume = (4/3)*pi*Rp^3
Ve  = earth volume = (4/3)*pi*R^3
Vp/Ve = Rp^3/R^3 = (2*R)^3/R^3 = 2^3 = 8
Vp = 8*Ve but the density is the same for both planets, so Mp = 8*M.

Escape velocity for planet = vp, then

vp*vp = G*Mp/Rp

the ratio of the escape velocities:

(vp*vp)/(ve*ve) = (G*Mp/(Rp))/(G*M/(R))
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substitute Mp = 8M and Rp = 2R, and G cancels.

= (8M/(2R))/(M/(r)) = 8/2 = 4

so (vp/ve)*(vp/ve) = 4

or vp = 2*ve

vp = 11*2 = 22 km/sec
Thank you
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Answer 2

your exact answer is 11×2=22