JEE Advanced Mi...

A metallic wire is shaped in the form of a circle with a radius of 2 cm and is placed on a horizontal non-conducting surface. A uniform magnetic field of B = 10 T is present in the region surrounding the circular wire and is directed vertically.

A conducting rod shown in red color, starting from x axis on the circular wire, slides along the wire while touching its length on the circumference of the circle. The equation of the circular wire is given as:

(x - 4)² + y² = 4

The rod moves with a uniform velocity, and the induced EMF in the rod reaches 5 V after 0.4 seconds.

Determine the velocity of the rod required to induce an EMF of 5 V in a magnetic field of 5 T after 0.4 seconds.

Aman has a rod of length ℓ meters . He wants to make a project on rotational motion and needs to check for the breaking stress of the rod. The rod has the following properties:

• Mass = 8.7 kg
• radius = 2 cm
• Breaking Strength (σ) = 8 × 10¹¹ Pa
• Angular frequency (ω) = 10⁶ rad/s

The rod is rotated about its center in a horizontal orientation . Aman wants to determine the maximum allowable length (ℓ) of the rod before it breaks due to rotational stress.

What should be the maximum value of ℓ to prevent breaking?

The internal energy (U) of an ideal gas depends on pressure (P) and volume (V) according to the equation:

P = 2UV^-1

Based on this equation, which of the following conclusions can be drawn about the gas?

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance R_P = 1Ω as shown in the figure. An external resistance of R_e = 2Ω is connected via the sliding contact.

Choose the correct answer from the options given below:

The major product in the following reaction is: