Introduction:
The long-term static modulus of elasticity is an important property of concrete that determines its ability to resist deformation under long-term loading. It is defined as the ratio of stress to strain in the elastic range of the stress-strain curve. The creep coefficient is a parameter that quantifies the long-term deformation of concrete due to sustained loading.

Calculation:
According to the provisions of IS:456-2000, the long-term static modulus of elasticity for M25 concrete with a creep coefficient of 1.5 can be calculated using the following formula:

E_long-term = E_instantaneous / (1 + creep coefficient)

Where:
E_long-term is the long-term static modulus of elasticity
E_instantaneous is the instantaneous modulus of elasticity

Substituting the values:
For M25 concrete, the instantaneous modulus of elasticity is typically around 5000 MPa. Substituting this value and the creep coefficient of 1.5 into the formula, we can calculate the long-term static modulus of elasticity as follows:

E_long-term = 5000 / (1 + 1.5)
E_long-term = 5000 / 2.5
E_long-term = 2000 MPa

Explanation:
The correct answer for the long-term static modulus of elasticity of M25 concrete with a creep coefficient of 1.5, as per the provisions of IS:456-2000, is 2000 MPa. This means that when subjected to sustained loading, the concrete will experience long-term deformation and its ability to resist deformation will be reduced to 2000 MPa.

The creep coefficient of 1.5 indicates that the long-term deformation of the concrete under sustained loading will be 1.5 times greater than the instantaneous deformation. This accounts for the time-dependent behavior of concrete and the gradual increase in deformation over time.

It is important to note that the long-term static modulus of elasticity is a property specific to each concrete mix and may vary depending on factors such as the type and quality of materials used, curing conditions, and environmental factors. Therefore, it is necessary to determine the specific value of the long-term static modulus of elasticity for each concrete mix through testing or reference to relevant standards.