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Two tiny spheres each of mass M and having charges q and -q are connected by a massless rod of length L . They are placed in a uniform electric field at angle theta with E .Calculate the minimum time in which the system aligns itself parallel to E?
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Two tiny spheres each of mass M and having charges q and -q are conne...
**Problem Statement**
Two tiny spheres, each of mass M and having charges q and -q, are connected by a massless rod of length L. They are placed in a uniform electric field at an angle theta with E. Calculate the minimum time in which the system aligns itself parallel to E.

**Solution**
When the system is placed in an electric field at an angle theta with E, the charges experience a torque that tries to align them with the E field. The system will keep rotating until the torque is balanced by the moment of inertia of the system. The minimum time required for the system to align itself parallel to E can be calculated using the following steps:

**Step 1: Calculate the torque on the system**

The torque on the system can be calculated using the following formula:

τ = r × F

where r is the vector from the center of mass of the system to the point of application of force and F is the force acting on the system. In this case, the force is the electric force acting on the charges. The torque can be expressed as:

τ = qELsinθ

where E is the magnitude of the electric field and θ is the angle between the electric field and the rod.

**Step 2: Calculate the moment of inertia of the system**

The moment of inertia of the system can be calculated using the formula:

I = 2MR²/5

where M is the mass of each sphere and R is the distance between the center of mass and the end of the rod. R can be calculated using the formula:

R = L/√3

**Step 3: Calculate the minimum time**

The minimum time required for the system to align itself parallel to E can be calculated using the formula:

t = (π/2)√(I/τ)

Substituting the values of I and τ, we get:

t = 2.27√(MqEL/5)

Therefore, the minimum time required for the system to align itself parallel to E is 2.27 times the square root of the product of the mass, charge, electric field, and rod length divided by 5.

**Conclusion**
In conclusion, the minimum time required for the system to align itself parallel to E can be calculated using the formula t = 2.27√(MqEL/5). This problem highlights the concept of torque and moment of inertia in rotational motion and can be solved using basic principles of physics.
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Two tiny spheres each of mass M and having charges q and -q are connected by a massless rod of length L . They are placed in a uniform electric field at angle theta with E .Calculate the minimum time in which the system aligns itself parallel to E?
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Two tiny spheres each of mass M and having charges q and -q are connected by a massless rod of length L . They are placed in a uniform electric field at angle theta with E .Calculate the minimum time in which the system aligns itself parallel to E? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two tiny spheres each of mass M and having charges q and -q are connected by a massless rod of length L . They are placed in a uniform electric field at angle theta with E .Calculate the minimum time in which the system aligns itself parallel to E? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two tiny spheres each of mass M and having charges q and -q are connected by a massless rod of length L . They are placed in a uniform electric field at angle theta with E .Calculate the minimum time in which the system aligns itself parallel to E?.
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