Two Masses 90 kg and 160 kg are separated by a distance of 5 m. The magnitude of intensity of the gravitational field at a point which is at a distance 3 m from the 90 kg mass and 4 m from the 160 kg mass is (Universal gravitational constant,
` G = 6.67 xx 10^(-11) N - m^(2) kg ^(-2)`).

Options

A. `94.3 xx 10^(-10) N kg ^(-1)`
B. `9.43 xx 10^(-10) N kg^(-1)`
C. `9.43 xx 10^(-12) N kg^(-1)`
D. `94.3 xx 10^(-12) N kg^(-1)`

Answer

B

Explanation

A system of two masses is shown in the figure,

Here, `m_(1) = 90` kg and
`m_(2) = 160` kg
Gravitational field intensity due to mass A,
`E_(A) = (GM_(A))/r_(CA)^(2) = G 90/((3^(2))) = 10 G hatr _(CA)`
Similarly, `E_(B) = G xx 160/4^(2) = 10 G hatr_(CB)`
In `Delta ABC,`
`(AB)^(2) = (AC)^(2) + (BC)^(2)`
` (5)^(2) = (3)^(2) + (4)^(2)`
Hence `Delta ABC ` is a right angle triangle.
Hence, the resultant of `E_(A) and E_(B)`.
`E = sqrt(E_(A)^(2) + E_(B)^(2))=sqrt((10G)^(2) + (10G)^(2) ) = sqrt(2) xx 10 G`
Putting the value of G, we get
`rArr E = sqrt(2)xx10xx6.67xx10^(-11)`
` = 9.43 xx 10^(-10)" Nkg"^(-1)`
Hence, the correct option is (b)