Question

Three identical point masses, each of mass 1kg lie in the x-y plane at points (0, 0), (0, 0.2m) and (0.2m, 0). The net gravitational force on the mass at the origin is

• A. $1.67 \times 10 ^ { - 9 } ( \hat { j } + \hat { j } ) N$
• B. $3.34 \times 10 ^ { - 10 } ( \hat { i } + \hat { j } ) N$
• C. $1.67 \times 10 ^ { - 9 } ( \hat { i } - \hat { j } ) N$
• D. $3.34 \times 10 ^ { - 10 } ( \hat { i } + \hat { j } ) N$

Answer 1

Answer: (A)

$1.67 \times 10 ^ { - 9 } ( \hat { j } + \hat { j } ) N$

Answer 2

Let particle $A$ lies at origin, particle $x$-axis respectively

$\overrightarrow { F _ { A C } } = \frac { G m _ { A } m _ { B } } { r _ { A B } ^ { 2 } } \hat { i }$ $= \frac { 6.67 \times 10 ^ { - 11 } \times 1 \times 1 } { ( 0.2 ) ^ { 2 } } \hat { i } = 1.67 \times 10 ^ { - 9 } \hat { i } N$

Similarly $\overrightarrow { F _ { A B } } = 1.67 \times 10 ^ { - 9 } \hat { j } N$

$\therefore$Net force on particle A $\vec { F } = \vec { F } _ { A C } + \vec { F } _ { A B } = 1.67 \times 10 ^ { - 9 } ( \hat { i } + \hat { j } ) N$