(a) Three objects of masses 10 kg, 12 kg and 15 kg are lying in a straight line

Question

(a) Three objects of masses 10 kg, 12 kg and 15 kg are lying in a
straight line such that the 15 kg object is in the middle, the 12
kg object to the right and 10 kg object to the left. If the
center to center distance of 10 kg and 15 kg object is 20 meters
and between 15 kg and 12 kg object is 30 meters, then find the
magnitude and direction of the NET FORCE acting on the object of mass
15 kg. Remember that force is a vector quantity and if you choose
force in one direction to be positive then the force in the opposite
to that direction will be negative.
(b) The radius of the moon is 4 times smaller than the radius of the
earth. Also, the mass of the moon is 8 times smaller than mass of the earth.Find the escape velocity from the surface of the moon.

Explanation / Answer

a) let the right direction be positive.
net force on the 15kg particle = (Gx10x15)/202 - (Gx15x12)/302 = 1.6x10-11 N (to the right)

 

b)escape velocity v= (2GM/R)

escape velocity of moon/escape velocity of earth = (1/(8 x 4))

we know escape velocity of earth = 11.2 km/s

escpae velocity of moon = 11.2km/s x  (1/(8 x 4)) = 1.98 km/s

(alternatively we can  directly substitute the mass and radius)

mass of earth  =5.972 x 1024 kg

radius of earth = 6378 km

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