AP EAMCET201921 Apr 2019Morning ShiftPhysicsGravitationActual
Two masses 90 ~kg and 160 ~kg are separated by a distance of 5 ~m . The magnitude of intensity of the gravitational field at a point which is at a distance 3 ~m from the 90 ~kg mass and 4 ~m from the 160 ~kg mass is (Universal gravitational constant, .G=6.67 10⁻¹¹ ~N - m ^2 ~kg ⁻² )
Options
- A94.3 10⁻¹⁰ ~N ~kg ⁻¹
- B9.43 10⁻¹⁰ ~N ~kg ⁻¹
- C9.43 10⁻¹² ~N ~kg ⁻¹
- D94.3 10⁻¹² ~N ~kg ⁻¹
Correct answer
B. 9.43 10⁻¹⁰ ~N ~kg ⁻¹
Step-by-step solution
A system of two masses is shown in the figure, Here, m₁=90 ~kg and m₂=160 ~kg Gravitational field intensity due to mass A , E _A= G M_A r _ C A ^2 =G 90 (3^2 ) =10 G r _ C A Similarly, E _B=G 160 4^2 =10 G r _ C B In A B C , aligned (A B)^2 & =(A C)^2+(B C)^2 (5)^2 & =(3)^2+(4)^2 aligned Hence A B C is a right angle triangle. Hence, the resultant of E _A and E _B , E= E_A^2+E_B^2 = (10 G)^2+(10 G)^2 = 2 10 G Putting the value of G , we get aligned E & = 2 10 6.67 10⁻¹¹ & =9.43 10⁻¹⁰ Nkg ⁻¹ aligned Hence, the correc