Gravitation.

Question 1

What is the formula of acceleration due to gravity on the surface of the earth ?

Answer 1

g= GM/R^

Question 2

What is the formula of acceleration due to gravity at a height h from the surface of the earth ?

Answer 2

g’= g( 1 - 2h/R) if h

Question 3

What is the acceleration due to gravity from the surface of the earth ?

Answer 3

g’= g(1-d/R); if d = R, then g’ = 0

Question 4

What is the formula for effect of rotation of earth at latitude ?

Answer 4

g'= g-Rω²cos² δ
At equator ,
δ=0, g'=g-Rω= minimum value.  
At poles,
δ= 90, cos 90=0, there g'= max value. 
At pole effect of rotation of earth is zero and g is maximum.

Question 5

What is the gravitational field strength at a point in a gravitational field ?

Answer 5

E= F/m= Gravitational force per unit area.

Question 6

What is the gravitational field strength due to a point mass ?

Answer 6

E= GM/r^

E~1/r^

Question 7

What is the gravitational field strengths due to a solid sphere ?

Answer 7

Inside points ie at centre
E= (GM/R³) r
At outside points 
E₀=GM/r²
On the surface , E-r graph is continuous.

Question 8

What is the gravitational field strength due to a spherical shell?

Answer 8

Inside points 
E(i)=0
Outside points 
E₀=GM/r²
Just outside the surface 
E=GM/R^
On the surface ,E-r graph is discontinuous.

Question 9

What is gravitational potential?

Answer 9

Gravitational potential at a point in a gravitational field is the negative of work done by gravitational force in moving a unit mass from infinity to that point.

Question 10

What is the gravitational potential to point mass ?

Answer 10

V=-GM/r

Question 11

What is the gravitational potential due to a solid sphere ?

Answer 11

Inside points:
V(i) = -GM÷R³(1.5R²−0.5r²)
On surface, V=-GM/R
At centre, V=-1.5GM/R
V-r graph is parabolic for inside points and potential at centre is 1.5times potential at surface. 
Outside points:
V=-GM/r

Question 12

What is the gravitational potential due to a spherical shell?

Answer 12

Inside points:
V(i)= -GM/R= constant
Outside points:
V=-GM/r

Question 13

What is the gravitational potential on the axis of the ring ?

Answer 13

V=−GM÷√R²+x²

Question 14

What is really gravitational potential energy for two point masses?

Answer 14

U=-Gm₁m₂÷r

Question 15

Why is the relation between field strength E and potential V if V is a function of only one variable (say r)?

Answer 15

E=-dV/dr=- slope of V-r graph

Question 16

What is the formula of escape velocity form the surface of the earth ?

Answer 16

V(e)= √2gR = √2GM/R~ 11.2 km/s

It does not depend upon the angle at which particle is projected from the earth.

Question 17

Formula of orbital speed Vo?

Answer 17

v₀=√GM/r

Question 18

For motion of satellites , formula of kinetic energy k?

Answer 18

K= GMm/2r

Question 19

For motion of satellites, formula of potential energy U?

Answer 19

U=-GMm/r

Question 20

For motion of satellites , formula for total mechanical energy ?

Answer 20

E=-GMm/2r

Question 21

What is the minimum time period of any earth satellite ?

Answer 21

84.6 min

Question 22

What is Kepler’ first law?

Answer 22

Kepler’s first law states that each planet moves in an elliptical orbit, with the sun at one focus of the ellipse.

Question 23

What is Kepler’s second law ?

Answer 23

Kepler’s second law states that the radius vector , drawn from sun to planet, sweeps out equal areas in equal time interval ie areal velocity is constant. This law is derived from the law of conservation of angular momentum.
dA/dt= L/2m= constant.

Question 24

What is Kepler’s third law ?

Answer 24

T² is directly proportional to r³ where r is a semi major axis of elliptical path.