The gravitational force between two bodies is a10N when they are kept at a distance of 4 m how much gravitational force is produced when they are kept 2 apart ​

Gravitational force F=

r

2

Gm

1

m

2

Case (i) : Mass of one object is doubled i.e m

1

′

=2m

1

∴ F

′

=

r

2

G(2m

1

)m

2

⟹F

′

=2F

Thus gravitational force gets also doubled

Case (ii) : Distance between the objects is doubled i.e r

′

=2r

∴ F

′

=

(2r)

2

Gm

1

m

2

⟹F

′

=

4

F

Thus gravitational force gets reduced by 4 times.

Distance between the objects is tripled i.e r

′

=3r

∴ F

′

=

(3r)

2

Gm

1

m

2

⟹F

′

=

9

F

Thus gravitational force gets reduced by 9 times.

Case (iii) : Mass of both the objects are doubled i.e m

1

′

=2m

1

and m

2

′

=2m

2

∴ F

′

=

r

2

G(2m

1

)(2m

2

)

⟹F

′

=4F

Thus gravitational force becomes 4 times.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

b.

explanation: