The free end of a simple pendulum is attached to the ceiling of a box. The box is taken to a height and the pendulum is oscillated. When the bob is at its lowest point the box is released to fall freely. As seen from the box during this period the bob will

Options

A. continue its oscillation as before
B. stop
C. will go in a circular path
D. move on a straight line

Answer

To solve the problem step by step, we will analyze the scenario of the pendulum bob inside the falling box.

### Step 1: Understand the Setup
We have a simple pendulum attached to the ceiling of a box. The box is initially at rest and is taken to a height. The pendulum is oscillated, and when the bob is at its lowest point, the box is released to fall freely.

**Hint:** Visualize the scenario by drawing the box and the pendulum. Identify the forces acting on the bob when the box is in free fall.

### Step 2: Identify Forces Acting on the Bob
When the box is released to fall freely, both the box and the pendulum bob experience the same gravitational acceleration (g). In the frame of reference of the box, the box is in free fall, and thus, it does not exert any normal force on the bob.

**Hint:** Remember that in free fall, all objects experience the same acceleration due to gravity.

### Step 3: Analyze the Motion of the Bob
In the frame of the box, which is a non-inertial frame (because it is accelerating downwards), we need to consider the effects of pseudo forces. The bob will experience a pseudo force acting upwards equal to its weight (mg) because the box is falling downwards.

**Hint:** Think about how forces balance out in a non-inertial frame. The pseudo force acts in the opposite direction of the acceleration of the frame.

### Step 4: Determine the Resultant Motion
At the lowest point of the pendulum's swing, the forces acting on the bob are:
- The gravitational force (downwards) = mg
- The pseudo force (upwards) = mg

Since these two forces cancel each other out, the only force acting on the bob is the inertia due to its horizontal velocity (if any).

**Hint:** Consider what happens to the motion of the bob when the forces cancel out.

### Step 5: Conclusion on the Motion of the Bob
Since the bob is not acted upon by any net vertical force, it will not oscillate as it would normally do. Instead, it will continue moving horizontally due to its initial velocity, following a straight line path.

**Hint:** Reflect on the concept of inertia: an object in motion will remain in motion unless acted upon by a net external force.

### Final Answer
As seen from the box during this period, the bob will move on a straight line.