A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than `90^(@)`. At its highest point, the string is cut. Which trajectory is possible for the bob afterwards ?

Options

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Answer

To solve the problem, we need to analyze the motion of the pendulum bob at the moment the string is cut. Here’s the step-by-step solution:

### Step 1: Understand the Initial Conditions
The pendulum bob is swinging in a vertical plane with an angular amplitude of less than 90 degrees. At its highest point in the swing, the bob momentarily comes to rest before the string is cut.

**Hint:** Remember that at the highest point of a pendulum swing, the velocity is zero.

### Step 2: Analyze Forces Acting on the Bob
When the string is intact, the forces acting on the bob include the tension in the string and the gravitational force (weight) acting downwards. At the highest point, the tension is at its minimum, but it is still present.

**Hint:** Consider what happens to the forces when the string is cut.

### Step 3: Effect of Cutting the String
Once the string is cut, the tension in the string becomes zero. The only force acting on the bob is its weight (mg), which acts downward.

**Hint:** Think about Newton's second law and how the absence of tension affects the motion of the bob.

### Step 4: Determine the Motion of the Bob
Since the only force acting on the bob after the string is cut is the gravitational force (mg), the bob will experience an acceleration equal to g (acceleration due to gravity) directed downward.

**Hint:** Remember that the direction of acceleration determines the direction of motion.

### Step 5: Conclude the Trajectory
At the moment the string is cut, the bob has zero velocity (it is at the highest point). With only gravitational force acting on it, the bob will begin to fall straight down under the influence of gravity. Therefore, the trajectory of the bob after the string is cut will be a straight vertical line downward.

**Hint:** Visualize the motion of an object in free fall to understand the trajectory.

### Final Answer
The possible trajectory for the bob after the string is cut is a straight downward path.