Which of the following statements are true about acceleration due to gravity ?
(a) 'g' decreases in moving away from the centre if `rgtR`
(b) 'g' decreases in moving away from the centre if `rltR`
( c ) 'g' is zero at the centre of earth
(d) 'g' decreases if earth stops rotating on its axis

Options

A. a & b
B. a, b & c
C. a & c
D. a, b, c & d

Answer

To determine which statements about acceleration due to gravity (g) are true, let's analyze each statement step by step.

### Step 1: Analyze Statement (a)
**Statement (a): 'g' decreases in moving away from the center if r > R**

- When we move away from the center of the Earth (i.e., at a height above the surface), the gravitational acceleration (g) does indeed decrease. This is because the formula for gravitational acceleration at a height (h) above the surface is given by:
\[ g' = g \left( \frac{R}{R+h} \right)^2 \]
where \( g \) is the acceleration due to gravity at the surface and \( R \) is the radius of the Earth. As \( h \) increases, \( g' \) decreases.

**Conclusion:** Statement (a) is **True**.

### Step 2: Analyze Statement (b)
**Statement (b): 'g' decreases in moving away from the center if r < R**

- When we move towards the center of the Earth (i.e., at a depth d), the gravitational acceleration decreases. The formula for gravitational acceleration at a depth (d) is:
\[ g' = g \left( 1 - \frac{d}{R} \right) \]
As we move deeper (increase d), \( g' \) decreases. However, if we are moving away from the center (i.e., towards the surface), \( g' \) increases.

**Conclusion:** Statement (b) is **False**.

### Step 3: Analyze Statement (c)
**Statement (c): 'g' is zero at the center of the Earth**

- At the center of the Earth, the gravitational forces from all directions cancel out, resulting in zero net gravitational acceleration. Therefore, the value of g at the center is indeed zero.

**Conclusion:** Statement (c) is **True**.

### Step 4: Analyze Statement (d)
**Statement (d): 'g' decreases if the Earth stops rotating on its axis**

- The effective gravitational acceleration (g') at the surface is influenced by the Earth's rotation. The centrifugal force due to rotation slightly reduces the effective value of g. If the Earth were to stop rotating, this centrifugal force would disappear, and the effective gravitational acceleration would increase, not decrease.

**Conclusion:** Statement (d) is **False**.

### Final Conclusion
The true statements about acceleration due to gravity are:
- **(a)** True
- **(b)** False
- **(c)** True
- **(d)** False

Thus, the correct options are **(a) and (c)**.

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