Question

A block of mass \( m \) and charge \( q \) is connected to a point 'O' with an inextensible string. This system is on a horizontal table. An electric field \( E \) is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field is:

• A. \( qE \)
• B. \( 2qE \)
• C. \( \frac{3qE}{4} \)
• D. \( 3qE \)

Hint:

In such problems, analyze the forces acting on the block and use the geometry of the system to balance the forces in different directions.

Answer 1

The Correct Option is D

When the block is subjected to an electric field, the force on the block due to the electric field is given by: \[ F = qE \] This force acts on the block in the direction of the electric field. Additionally, there is a tension \( T \) in the string that prevents the block from accelerating along the surface. The tension in the string is a vector, and its component parallel to the electric field must balance the force due to the electric field. When the string becomes parallel to the electric field, the tension \( T \) in the string balances the electric force: \[ T = 3qE \] Thus, the correct answer is option (4), \( 3qE \).

Answer 2

Step 1: Understanding the setup
A block with mass \( m \) and charge \( q \) is tied to a fixed point 'O' by a string on a horizontal table.
An electric field \( E \) is applied perpendicular to the string initially and lies in the table’s plane.

Step 2: Forces acting on the block
The forces on the block are:
- Tension \( T \) in the string,
- Electric force \( F_e = qE \) acting due to the electric field,
- Normal reaction and weight balance vertically and are not affecting horizontal motion.

Step 3: When the string becomes parallel to the electric field
At this position, the tension \( T \) must balance the resultant forces acting on the block.
If the block moves under electric force and tension, consider the equilibrium of forces in the direction of the string.

Step 4: Calculating tension
The net force due to electric field when the string is parallel is \( qE \). The tension \( T \) must provide the necessary force to keep the block in circular motion and balance the electric force.
By vector addition of forces and equilibrium conditions, tension \( T = 3 q E \).

Step 5: Conclusion
Therefore, the tension in the string when it becomes parallel to the electric field is \( 3 q E \).