42 A straight rod of mass m and length L is suspended from the identic

1.	42 A straight rod of mass m and length L is suspended from the identical spring as shown in the figure. Thespring stretched by a distance of x, due to the weight of the wire. The circuit has total resistance RQ.When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed toextend further by the same distance. The magnetic field strength isdirected outward from the plane of the paper28 x, i directed outward from the plane of the paper(C) BL directed into the plane of the paper(D) mgR, directed into the plane of the paper
Answer» (c ) [(mgR) / (LV)] is correct. Force exerted by spring =ky0. As weight is divided between two spring, 2(ky0) = weight = mg ∴ky0= (mg /2)(1) alsoI = (V/R)(2) Fm= magnetic force on the rod = BIℓ from (2) Fm= [(BLV) / R](3) When field is ON, spring are observed to extend further. ∴mg + Fm= 4ky0 Fm= 4ky02ky0from(1) Fm= 2ky0 from (3) [(BLV) / R] = 2ky0 ∴B = [(2ky0R) / (LV)] from (1) putting 2ky0= mg ∴B = [(mgR) / LV] no the ans is option 2

42 A straight rod of mass m and length L is suspended from the identical spring as shown in the figure. Thespring stretched by a distance of x, due to the weight of the wire. The circuit has total resistance RQ.When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed toextend further by the same distance. The magnetic field strength isdirected outward from the plane of the paper28 x, i directed outward from the plane of the paper(C) BL directed into the plane of the paper(D) mgR, directed into the plane of the paper

Answer»

(c ) [(mgR) / (LV)] is correct.

Force exerted by spring =ky0. As weight is divided between two spring,

2(ky0) = weight = mg

∴ky0= (mg /2)(1)

alsoI = (V/R)(2)

Fm= magnetic force on the rod = BIℓ

from (2) Fm= [(BLV) / R](3)

When field is ON, spring are observed to extend further.

∴mg + Fm= 4ky0

Fm= 4ky02ky0from(1)

Fm= 2ky0

from (3)

[(BLV) / R] = 2ky0

∴B = [(2ky0R) / (LV)]

from (1) putting 2ky0= mg

∴B = [(mgR) / LV]

no the ans is option 2