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Explain principle of super position forgravitational force. |
Answer» Solution :`implies` The net gravitational force on a particle is the vector sum of the INDIVIDUAL gravitational FORCES on the particle.  `implies` Gravitational force on point mass `m_1` due to point mass `m_2` `vecF_(12)=G(m_1m_2)/(|vecr_(12)|).hatr^2""`or `vecF_(12)=(-Gm_(1)m_(2))/(|vecr_(21)|)^2.hatr_(21) ""...(1)` `hatr_(12)` is a UNIT vector from `m_(1) "to " m_2` `hatr_(21)` is a unit vector from `m_(2) "to " m_1` `implies` Gravitational force of mass `m_1` due to mass `m_3` `vecF_(13)=(Gm_1m_3)/(|vecr_(13)|).hatr_(13)=(-Gm_(1)m_(2))/(|vecr_(31)|^2)hatr_(31)""...(2)` `implies` Gravitational force of mass `m_1` due to mass `m_4` `vecF_(14)=(Gm_1m_4)/(|vecr_(14)|).hatr_(14)=(-Gm_(1)m_(4))/(|vecr_(41)|^2)hatr_(41)""...(3)` `implies` The TOTAL force on `m_1` `vecF_(1)=(Gm_1m_2)/(|vecr_(12)|).hatr_(12)+G(m_(1)m_(2))/(|vecr_(13)|^2)hatr_(31)+(Gm_(1)m_(4))/(|vecr_(14)|^2)""...(4)` `vecF_(1)=-((Gm_1m_2)/(|vecr_(21)|).hatr_(21)+G(m_(3)m_(1))/(|vecr_(31)|^2)hatr_(31)+(Gm_(4)m_(1))/(|vecr_(41)|^2)hatr_(41))""..(5)` Note : The gravitational field intensity is the force on a unit mass at a point in the field. |
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