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Physics Question on Newtons law of gravitation

Two identical objects each of mass 50 kg50 \,kg are kept at a distance of separation of 50 cm50\, cm apart on a horizontal table. The net gravitational force at the mid-point of the line joining their centres is

A

zero

B

6.6733×10−9N6.6733 \times 10^{-9}N

C

13.346×10−9N 13.346 \times 10^{-9}N

D

3.336×10−9N 3.336 \times 10^{-9}N

Answer

zero

Explanation

Solution

The net gravitational force between two objects depends on their masses and the distance between them. The formula for gravitational force is given by :
F=G×(m1×m2)r2F = \frac{G \times (m_1 \times m_2) }{ r^2}
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
In this case, the two objects are identical and have the same mass, m1 = m2 = 50 kg.
The distance between them is r = 50 cm = 0.5 m.
The gravitational force between the two objects is:

F=G×(m1×m2)r2=6.6733×10−11×(50×50)(0.5×0.5)=6.6733×10−9NF = \frac{G \times (m1 \times m2) }{r^2} = \frac{6.6733×10^{−11} \times (50 \times 50)} {(0.5 \times 0.5)} = 6.6733×10^{−9} N
The gravitational force on each object due to the other is equal in magnitude and opposite in direction. Therefore, the net gravitational force at the mid-point of the line joining their centres is zero.
Hence, the correct answer is zero.
So, the correct option is (A) : Zero.