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Motion In Straight Line

Question
CBSEENPH11017640
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Two masses of 25 kg and 75kg are separated by a distance of 20m. Find the gravitational field strength at a point at a distance of 5 m from 25kg mass.

Solution

Given,

Mass space of space the space first space body comma space straight M subscript 1 equals 25 kg Mass space of space the space second space body comma space straight M subscript 2 equals 75 kg 
Distance between the two bodies = 20 m 
Distance space of space mass space straight m subscript 1 space end subscript from space 25 space kg comma space straight r subscript 1 equals 5 straight m Distance space of space mass space straight m subscript 2 space from space 25 kg comma space straight r subscript 2 equals 15 straight m 
Let space space straight E subscript 1   and space space straight E subscript 2  be the gravitational field strength due to masses 25 kg and 75 kg respectively. 
Using the formula, we have
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               space equals 6.66 cross times 10 to the power of negative 11 end exponent straight N divided by kg 

straight E subscript 2 equals GM subscript 2 over straight r subscript 2 squared equals fraction numerator 6.66 cross times 10 to the power of negative 11 end exponent cross times 75 over denominator 225 end fraction 
              space equals 2.22 space cross times space 10 to the power of negative 11 end exponent straight N divided by kg 
Since straight E subscript 1 space and space straight E subscript 2 are in opposite direction, therefore net field strength at given point is, 
           straight E equals straight E subscript 1 minus straight E subscript 2 equals 4.44 cross times 10 to the power of negative 11 end exponent straight N divided by kg

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