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Gravitational Force

Two masses ...

Question

Two masses $90$ kg and $160$ kg are at a distance $5$ m apart. Compute the magnitude of intensity of the gravitational field at a point distance $3$ m from the $90$ kg and $4$ m from the $160$ kg mass. G $= 6.67 \times 10^{- 11} k g^{- 2}$ .

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Solution

Let A and B be the positions of the masses and P be the point at which the gravitational intensity is to be computed.
Gravitational intensity at P due to mass at A will be
$E_{A} = G \frac{90}{3^{2}} = 10 G$ , along PA.
Gravitational intensity at P due to mass at B will be
$E_{B} = G \frac{160}{4^{2}} = 10$ G, along PB.
In $Δ$ APB, $A B^{2} = A P^{2} + P B^{2}$ $(∴ ∠ A P B = 90^{o})$
Therefore, the magnitude of resultant gravitational intensity at P will be
$E = \sqrt{E_{A}^{2} + E_{B}^{2}} = \sqrt{(10 G)^{2} + (10 G)^{2}} = 10 \sqrt{2} G$
$= 10 \sqrt{2} \times 6.67 \times 10^{- 11}$ N/kg $= 9.43 \times 10^{- 10}$ N $k g^{- 1}$ .

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Two masses 90kg and 160kg are at a distance 5m apart. Compute the magnitude of intensity of the gravitational field at a point distance 3m from the 90kg and 4m from the 160kg mass. G=6.67×10−11kg−2.

Two masses $90$ kg and $160$ kg are at a distance $5$ m apart. Compute the magnitude of intensity of the gravitational field at a point distance $3$ m from the $90$ kg and $4$ m from the $160$ kg mass. G $= 6.67 \times 10^{- 11} k g^{- 2}$ .