SINGLE CHOICE

1. A conducting rod is rotated in uniform magnetic force field (B)

with constant velocity (V). Thep.d. is developed between ends of rod when

a) V||l b) V||B c) l||B d) None

2. Inbinary system 111 represents—

a) 1 b) 3 c) 7 d) 100

3. Which of the following help us for recognition of precious stone

a) UV rays b) Infrared c) X- rays d) None

4. If two conducting spheres are connected after charging separately then—

a) both sphere energy will remain conserved

b) both charge remains conserved

c) both energy & charge remain conserved

d) None

MORE THAN ONE CHOICE

5. According to Bohr's theory of h ydrogen atom

a) (linear momentum is proportionel to 1/n

b) (the radius is proportionel to n)

c) (the K.E. is proportional to 1/n2

d) the angular momentum is proportional to n

6. A point object is placed at 30 cm from a convex glass lens (mu g = 3/2{ (refractive index) } of focal length 20 cm. The final image of

object will be formed at infinity if

a) another concave lens of focal length 60 cm is placed in contact with the previous lens

b) another conves lens of focal length 60 cm is placed at distance of 30 cm from the first lens

c) the whole system is immersed in a liquid of refractive index 4/3

d) the whole system is immersed ina liquid of refractive index 9/8

7. If a charged particle at rest experiences no electromagnetic force then

a) Electric field must be zero)

b) Magnetic field must be zero]

c) Electric field may or may not be zero

d) Magnetic field may or may not be zero

Let's break down your questions one by one, providing clear explanations and reasoning for each. This will help you understand the concepts behind them and how to approach similar problems in the future.

1. Conducting Rod in a Magnetic Field

When a conducting rod is rotated in a uniform magnetic field, a potential difference (p.d.) is induced across its ends due to electromagnetic induction. The correct answer here is b) V||B. This is because the motion of the rod must be perpendicular to the magnetic field lines to generate a p.d. If the velocity of the rod is parallel to the magnetic field, no p.d. will be induced.

Explanation of Electromagnetic Induction

According to Faraday's law of electromagnetic induction, a change in magnetic flux through a circuit induces an electromotive force (emf). In this case, the motion of the rod through the magnetic field creates a change in flux, leading to the generation of voltage. If the rod moves parallel to the magnetic field (V||B), it does not cut through the magnetic lines of force, resulting in no induced emf.

2. Binary System Representation

In the binary system, the number 111 represents c) 7. Each digit in binary represents a power of 2, so:

• 1st digit (from the right) = 1 × 2^0 = 1
• 2nd digit = 1 × 2^1 = 2
• 3rd digit = 1 × 2^2 = 4

Adding these together gives 1 + 2 + 4 = 7.

3. Recognition of Precious Stones

To recognize precious stones, the correct choice is a) UV rays. Ultraviolet light can reveal unique fluorescence properties of certain gemstones, which helps in their identification.

How UV Rays Work

When exposed to UV light, some gemstones will emit visible light, making it easier to distinguish them based on their fluorescence. For example, diamonds may fluoresce blue under UV light, while other stones may show different colors or no fluorescence at all.

4. Conducting Spheres and Charge Conservation

When two conducting spheres are connected after being charged separately, the correct answer is c) both energy & charge remain conserved. Charge will redistribute between the spheres, but the total charge and energy in the system will remain constant.

Understanding Charge Redistribution

When the spheres are connected, charge flows until they reach the same potential. While the individual charges may change, the total charge before and after connection remains the same. Energy may change due to the redistribution of charge, but the total energy in the system is conserved.

5. Bohr's Theory of Hydrogen Atom

According to Bohr's theory, the correct statements are a) linear momentum is proportional to 1/n and c) K.E. is proportional to 1/n². The angular momentum is quantized and proportional to n, but the radius is not directly proportional to n; it is proportional to n².

Bohr's Model Insights

In Bohr's model, the quantization of angular momentum leads to specific energy levels for electrons in an atom. The kinetic energy of the electron decreases as the principal quantum number n increases, which is why it is proportional to 1/n².

6. Image Formation with Lenses

For the scenario with the convex lens and the object, the correct answer is a) another concave lens of focal length 60 cm is placed in contact with the previous lens. This setup can create a system where the final image is formed at infinity.

Combining Lenses

When a concave lens is placed in contact with a convex lens, the effective focal length of the system can be calculated. If the combined focal length is positive and the object is placed at the right distance, the final image can be formed at infinity.

7. Charged Particle at Rest

If a charged particle at rest experiences no electromagnetic force, the correct answer is c) Electric field may or may not be zero. The magnetic field does not exert a force on a stationary charge.

Electromagnetic Forces Explained

The force on a charged particle is given by the Lorentz force law, which states that the force is dependent on both electric and magnetic fields. If the particle is at rest, the magnetic field does not contribute to the force, but the electric field can still be present or absent.

These explanations should help clarify the concepts behind each question. If you have any further questions or need more examples, feel free to ask!