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The position vector of the objects of ma...

The position vector of the objects of masses 25 kg and 10 kg are (4,7,5)m and (1,3,5) m respectively. Obtain the vector representing the gravitational force on 25 kg object by 10 kg object. (Take `G = 6.67 xx 10^(-11) Nm^(2)kg^(-2) )`

Text Solution

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`implies` Here , `m_1 = 25 kg , m_2 = 10 kg `
`vecr_1 = (4,7,5) m, vecr_2 = (1,3,5) m, vecF_(12) = (?)`
`vecF_(12) = G(m_1m_2)/(r^2) hatr_(12) " "....(1)`
`vecr_(12) = vecr_(2) - vecr_(1)= (1,3,5) - (4,7,5) = (-3, -4,0) m `
`:. r = |vecr_(12)|=sqrt((-3)^2+(-4)^2+(0)^2)=5m`
and ` vecr_(12) = (vecr_(12))/(|vecr_(12)|)=((-3,-4,0))/5`
`= (0.6, -0.8 ,0)`
`= 0.6 hati - 0.8 hatj`
Putting this in equation (1) ,
`vecF_(12)=(6.67 xx10^(-11))((25)(10))/(5^2) xx(-0.6 , 0.8 , 0)`
`= 6.67 xx 10^(-10)(0.6 hati - 0.8 hatj) N`
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