Gravitational Field Intensity or Gravitational Strength at a point is defined as the gravitational force exerted on a unit mass placed at that point.

Mathematically,

Gravitational Field Intensity or Gravitational Strength = GM /r²
where G = Gravitational Constant, M = mass and r = distance from the centre of the body to the point.

Dimensional Formula of Universal Constant of Gravitation = M^-1L³T^-2
Dimensional Formula of Mass = M¹L⁰T⁰
Dimensional Formula of Radius = M⁰L¹T⁰

Substituting in the above equation we get,
Dimensional Formula of Gravitational Field Intensity or Gravitational Strength = M⁰L¹T^-2
SI unit of Gravitational Field Intensity or Gravitational Strength is N kg^-1 or it can also be written as m s^-1

Note: Gravitational Field Intensity is often referred as Gravitational Field.

Spring Constant is defined as restoring force per unit displacement. Force is directly proportional to the displacement of the system. It can also be stated as force needed to compress or extend a spring is directly proportional to the displacement of the spring.

Mathematically,

Spring Constant = Force/Displacement

Dimensional Formula of Force = M¹L¹T^-2
Dimensional Formula of Displacement = M⁰L¹T⁰

So Dimensional Formula of Spring Constant = M¹L⁰T^-2
SI unit of Spring Constant is Nm^-1

Tensile Modulus , Modulus of Elasticity, Young modulus is defined as the stress required to cause a unit strain in the material. It is the ratio of linear stress to linear strain.

Mathematically,

Tensile Modulus , Modulus of Elasticity, Young modulus = linear stress / linear strain.

Dimensional Formula of linear stress = M¹L^-1T^-2
Dimensional Formula of linear strain = M⁰L⁰T⁰

Substituting in the above equation we get,

Dimensional Formula of Tensile Modulus , Modulus of Elasticity, Young modulus = M¹L^-1T^-2
SI unit of Tensile Modulus , Modulus of Elasticity, Young modulus = N m^-2

Poisson’s Ratio is defined as the ratio of lateral contraction to linear elongation . It can also be defined as the ratio of unit transverse (Lateral) strain to unit longitudinal strain.

Mathematically,
Poisson’s ratio (σ) = Lateral Strain / longitudinal strain.

Since we have different form of strain in the above equation and Dimensional Formula of Strain = M⁰L⁰T⁰.

And we know that ratio of dimensionless quantity is Dimensionless.

Therefore, Poisson’s ratio is Dimensionless and has no SI unit.

Angle is defined as the ratio of length of arc to radius.

Mathematically,

Angle = Length of Arc / Radius

Dimensional formula of Length = M⁰L¹T⁰
Dimensional formula of Radius = M⁰L¹T⁰

Substituting in the above formula we get,
Dimensional formula of Angle = M⁰L⁰T⁰. We can also say Angle is dimensionless quantity.
SI unit of Angle is radian (rad)