Question

Mass M is distributed uniformly over a rod of length L. Find the gravitational field at P at a distance a on perpendicular bisector.

• A.
• B.
• C.
• D. None of these

Answer 1

Answer: (B)

Answer 2

dm =

dE = $\int \mathrm { dE } \cos \theta = \frac { \mathrm { GMa } } { \mathrm { L } } \int _ { - 1 / 2 } ^ { 1 / 2 } \frac { \mathrm { dx } } { \left( \mathrm { x } ^ { 2 } + \mathrm { a } ^ { 2 } \right) ^ { 3 / 2 } }$Put x = a tan θ then dx = a sec² θ dθ

E =

= $\frac { \mathrm { GM } } { \mathrm { La } } \sin \theta = \left. \frac { \mathrm { GMx } } { \mathrm { La } \sqrt { \mathrm { x } ^ { 2 } + \mathrm { a } ^ { 2 } } } \right| _ { - 1 / 2 } ^ { 1 / 2 }$.

=