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) )

The position vector of the objects of masses 25 kg and 10 kg are (4,7,

1.	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) )
Answer» Solution :`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`