A simple pendulum having bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. The car moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some the top of the cliff. The tension in the string when the car is in air is

Options

A. `mg`
B. `mg-(mv^2)/R`
C. `mg+(mv^2)/R`
D. zero

Answer

To solve the problem, we need to analyze the forces acting on the pendulum bob when the car is in the air. Here are the steps to arrive at the solution:

### Step 1: Understand the scenario
The car is moving up an incline and then jumps off the cliff. While in the air, the only force acting on the pendulum bob is gravity, as there is no normal force from the car.

**Hint:** Remember that when the car is in the air, it is in free fall, and the only force acting on the pendulum bob is its weight.

### Step 2: Identify the forces acting on the pendulum bob
When the car is in the air, the forces acting on the bob are:
- The gravitational force (weight) acting downward, which is \( mg \).
- The tension in the string acting upward, which we will denote as \( T \).

**Hint:** Draw a free-body diagram to visualize the forces acting on the bob.

### Step 3: Apply Newton's second law
Since the car (and thus the pendulum bob) is in free fall, the net force acting on the bob is equal to its weight. The acceleration of the bob is equal to \( g \) (acceleration due to gravity), directed downward.

Using Newton's second law:
\[ \text{Net force} = m \cdot a \]
Here, \( a = g \), so:
\[ mg - T = mg \]

**Hint:** Consider the direction of the forces and remember that the net force must equal the mass times acceleration.

### Step 4: Set up the equation
From the equation above, we can rearrange it to find the tension \( T \):
\[ mg - T = mg \implies T = 0 \]

**Hint:** The tension is zero when the forces are balanced and the bob is in free fall.

### Step 5: Conclusion
Thus, the tension in the string when the car is in the air is:
\[ T = 0 \]

**Final Answer:** The tension in the string when the car is in air is \( 0 \).