Question

A straight rod of mass m and length L is suspended from the two identical springs as shown in figure. The spring is stretched a distance y0 due to the weight of the wire. The circuit has total resistance R. when the magnetic field perpendicular to the plane of paper is switched on, springs are observed to extend further by the same distance y0 the magnetic strength is ___

(a) [(2 mgR)/LV]

(b) [(mgR)/(LV)]

(c) [(mgR)/(2LV)]

(d) [(mgR)/(V)]

Answer 1

The correct option (b) [(mgR)/(LV)]

Explanation:

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

2(ky0) = weight = mg

∴ ky0 = (mg/2) (1)

Also I = (V/R) (2)

Fm = magnetic force on the rod = BIℓ

From (2) Fm = [(BLV)/R]

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

∴ mg + Fm = 4ky0

Fm = 4ky0 – 2ky0 from (1)

Fm = 2ky0

From (3)

[(BLV)/R] = 2ky0

∴ B = [(2ky0R)/(LV)]

From (1) putting 2ky0 = mg

∴ B = [(mgR)/LV]