Q51 / 51 · JEE Advanced 2023 (Paper 1) · Physics
A thin conducting rod of mass , length and resistance is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time and it moves down along the rails. Assume air drag is negligible. Match each quantity in List- with an appropriate value from List-, and choose the correct option.
[Given: The acceleration due to gravity and ]

List- List- At , the magnitude of the induced emf in Volt At , the magnitude of the magnetic force in Newton At , the power dissipated as heat in Watt The magnitude of terminal velocity of the rod in
A thin conducting rod of mass , length and resistance is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time and it moves down along the rails. Assume air drag is negligible. Match each quantity in List- with an appropriate value from List-, and choose the correct option.
[Given: The acceleration due to gravity and ]

| List- | List- | ||
| At , the magnitude of the induced emf in Volt | |||
| At , the magnitude of the magnetic force in Newton | |||
| At , the power dissipated as heat in Watt | |||
| The magnitude of terminal velocity of the rod in | |||
- A
- B
- C
- Correct answerD
Solution
Induced emf
Induced current
Direction of induced current would be from .
Now magnetic force acting on the rod due to this current would be in the upward direction. Therefore, we can write
[Applying law]
Now, , and
Therefore,
At
volts
Then, current at will be
and magnetic force
and power dissipated
also for maximum velocity(terminal velocity) and hence
Correct match is (D)
Hence, the correct answer is option: 'D'.
