Two bodies A and B having masses 20 kg and 40 kg are separated 10 M at what distance from body A should another body C of mass 15 kg we place so that the net gravitation force on C is zero? Explain in detail.




In this problem, we have to find the distance at which another body C of mass 15 kg should be placed from body A so that the net gravitational force on C is zero. To solve this problem, we need to use the concept of gravitational force and Newton's law of gravitation.



According to Newton's law of gravitation, the gravitational force between two objects of masses m1 and m2 separated by a distance r is given by:

F = G * (m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of two objects, and r is the distance between them.

Now, the net gravitational force on body C will be the vector sum of gravitational forces due to bodies A and B. Therefore, the net gravitational force on body C will be zero if the gravitational forces due to bodies A and B are equal in magnitude and opposite in direction.



Let's assume that body C is placed at a distance x from body A. Therefore, the distance between body C and body B will be (10 - x).

Now, using Newton's law of gravitation, we can calculate the gravitational forces due to bodies A and B on body C as follows:

F1 = G * (m1 * m3) / x^2

F2 = G * (m2 * m3) / (10 - x)^2

where F1 and F2 are the gravitational forces due to bodies A and B, respectively, and m3 is the mass of body C.

As per the problem, the net gravitational force on body C is zero. Therefore, we can write:

F1 = F2

G * (m1 * m3) / x^2 = G * (m2 * m3) / (10 - x)^2

Solving this equation, we get:

x = 2.5 m

Therefore, the distance from body A at which we should place body C of mass 15 kg is 2.5 m.



Thus, we can conclude that if we place body C of mass 15 kg at a distance of 2.5 m from body A, then the net gravitational force on body C will be zero.

Let the body C of mass 15 kg be held at a distance x from body A. as net gravitational force on C is zero,
therefore, F 1 = F 2 F1=F2
G × 20 × 15 x 2 = G × 15 × 40 /( 10 − x )
1/ x = √ 2 /10 − x
√ 2 x = 10 − x
1.414x+x=10
x = 10 /2.414
= 4.14 m