TS EAMCET 5-Aug-2021 Shift 2 Question Paper

Given,
Distance of point mass from rod be d. Let dm be the mass of element dx at distance x from start dm be the elemental length and mass.
Now, mass of element dx,dm=‌

M

L

dx
The separation between point mass and element will be (r+x).
As we know that,
F=‌

GM1M2

d2

where, F= gravitational force,
G= gravitational constant M1 and M2 be the masses and d be the separation between M1,M2.
∴‌‌dF (elemental force )=‌

Gdm⋅m

(r+x)2

On integrating both sides, we get
⇒‌‌

F

∫

0

dF‌‌=

L

∫

0

‌

GM∕Ldx⋅m

(r+x)2

F‌‌=‌

GMm

L

‌

L

∫

0

‌

dx

(r+x)2

‌‌=‌

GMm

L

⋅[−(r+x)−1]0L
‌‌=−‌

GMm

L

[‌

1

r+L

−‌

1

r

]
‌‌=−‌

GMm

L

[‌

r−r−L

r(r+L)

]=‌

GMm

r(r+L)

Magnitude of gravitational force, F=‌

GMm

r(r+L)