A body is being raised to a height h from the surface of earth. What is the sign of work done by
(a) applied force (b) gravitational force ?

Options

A. Positive, Positive
B. Positive, Negative
C. Negative, Positive
D. Negative, Negative

Explanation

To solve the question regarding the work done by the applied force and the gravitational force when a body is raised to a height \( h \) from the surface of the Earth, we can follow these steps:

### Step 1: Understand the Forces Involved
When a body is raised, two main forces are acting on it:
- An **applied force** acting upwards (in the direction of displacement).
- A **gravitational force** acting downwards (opposite to the direction of displacement).

### Step 2: Calculate Work Done by the Applied Force
The work done \( W \) by a force is given by the formula:
\[ W = F \cdot S \cdot \cos(\theta) \]
Where:
- \( F \) is the magnitude of the force,
- \( S \) is the displacement,
- \( \theta \) is the angle between the force and the displacement.

In this case:
- The applied force is in the upward direction.
- The displacement is also in the upward direction.
- Therefore, \( \theta = 0^\circ \).

Using the cosine of 0 degrees:
\[ \cos(0^\circ) = 1 \]
Thus, the work done by the applied force is:
\[ W_{applied} = F \cdot S \cdot 1 = F \cdot S \]
Since both \( F \) and \( S \) are positive, the work done by the applied force is **positive**.

### Step 3: Calculate Work Done by the Gravitational Force
Now, we calculate the work done by the gravitational force. Again using the formula:
\[ W = F \cdot S \cdot \cos(\theta) \]
In this case:
- The gravitational force acts downwards.
- The displacement is upwards.
- Therefore, \( \theta = 180^\circ \).

Using the cosine of 180 degrees:
\[ \cos(180^\circ) = -1 \]
Thus, the work done by the gravitational force is:
\[ W_{gravity} = F \cdot S \cdot (-1) = -F \cdot S \]
Since the gravitational force acts in the opposite direction to the displacement, the work done by the gravitational force is **negative**.

### Final Results
- (a) The sign of work done by the applied force is **positive**.
- (b) The sign of work done by the gravitational force is **negative**.