Chapter 13: Q.37 Excercises And Problems (page 354)

What is the total gravitational potential energy of the three masses in FIGUREP13.35?

Short Answer

Expert verified

The total gravitational potential energy isUnet=18.14×10-8J

Step by step solution

01

Given information 

mass of ball 1,m1=5.0kg

mass of ball 2,m2=20.0kg

mass of ball 3, m3=10.0kg

distance between ball 1and 2l1=20cm=0.2m

distance between ball 2and 3l2=10cm=0.1m

Newton's gravitational constantG=6.67×10-11m3/kgs2

02

Explanation

From the given FIGUREP13.35, the distance between mass1and3will be calculated by Pythagoras theorem,l3=l12+l22=(0.2)2+(0.1)2=0.22m

the gravitational potential energy for mass 1to 2is calculated as, U1-2=Gm1m2l1=6.67×10-11×5×200.2=3.3×10-8J

The gravitational potential energy for mass 2to 3is calculated as,

U2-3=Gm2m3l2=6.67×10-11×20×100.1=13.34×10-8J

The gravitational potential energy for mass 1to 3is calculated as,

U1-3=Gm1m3l3=6.67×10-11×5×100.22=1.5×10-8J

The total gravitational potential energy

Unet=U1-3+U1-2+U2-3=(3.3+13.34+1.5)×10-8J=18.14×10-8J

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