Suppose universal gravitational constant starts to decrease, then

Options

A. length of the year will increase
B. earth will follow a spiral path of decreasing radius
C. kinetic energy of earth will decrease
D. all of the above

Answer

To solve the problem regarding the effects of a decreasing universal gravitational constant (G), we will analyze the implications on various factors, particularly focusing on the length of the year and the kinetic energy of the Earth.

### Step-by-Step Solution:

1. **Understanding the Time Period of Earth's Orbit**:
- The time period (T) of Earth's orbit around the Sun can be expressed using Kepler's third law, which states:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
- Here, \(r\) is the radius of the orbit, \(G\) is the gravitational constant, and \(M\) is the mass of the Sun.

2. **Effect of Decreasing G on the Time Period**:
- If the gravitational constant \(G\) decreases, we can analyze how \(T\) is affected:
\[ T \propto \sqrt{\frac{1}{G}} \]
- Therefore, if \(G\) decreases, \(T\) (the time period) will increase. This means that the length of the year will also increase.

3. **Conclusion for Option A**:
- Since the time period of revolution increases with a decrease in \(G\), we conclude that **the length of the year will increase**. Thus, Option A is correct.

4. **Analyzing the Radius of Orbit**:
- As \(G\) decreases, the gravitational force between the Earth and the Sun also decreases. Consequently, the Earth will move to a larger orbit (larger radius) to maintain balance in the gravitational pull.
- Therefore, the radius of the Earth's orbit will increase, making Option B (the radius of the orbit decreases) incorrect.

5. **Kinetic Energy of the Earth**:
- The kinetic energy (K) of the Earth in its orbit can be expressed as:
\[ K = \frac{1}{2} mv^2 \]
- The orbital velocity \(v\) can be derived from the gravitational force:
\[ v = \sqrt{\frac{GM}{r}} \]
- Substituting this into the kinetic energy equation gives:
\[ K \propto G \]
- If \(G\) decreases, the kinetic energy \(K\) will also decrease.

6. **Conclusion for Option C**:
- Since the kinetic energy decreases with a decrease in \(G\), Option C is also correct.

### Final Answers:
- **Option A**: The length of the year will increase (Correct).
- **Option B**: The radius of the orbit decreases (Incorrect).
- **Option C**: The kinetic energy of the Earth will decrease (Correct).