A metallic rod of mass unit length 0.5 kg m -1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. A magnetic field of strength 0.25 T is acting on it in the vertical direction. When a current ' T ' is flowing through it, the rod is not allowed to slide down. The quantity of current required to keep the rod stationary is

Question

A metallic rod of mass unit length 0.5 kg m -1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. A magnetic field of strength 0.25 T is acting on it in the vertical direction. When a current ' T ' is flowing through it, the rod is not allowed to slide down. The quantity of current required to keep the rod stationary is (A) 14.76 A (B) 11.32 A (C) 7.14 A (D) 5.98 A

Tardigrade Admin · Accepted Answer

F = Bil Bil cos θ= mg sin θ 0.25 × I × (√3/2)=0.5 × 10 × (1/2) I =(5 × 100/25 × √3)=(20/√3) A I =11.32 A

14.76 A

11.32 A

7.14 A

5.98 A

F=Bil Bilcosθ=mgsinθ 0.25×I×23​​=0.5×10×21​ I=25×3​5×100​=3​20​A I=11.32A

$F = B i l$
$B i l cos θ = m g sin θ$
$0.25 \times I \times \frac{3}{2} = 0.5 \times 10 \times \frac{1}{2}$
$I = \frac{5 \times 100}{25 \times 3} = \frac{20}{3} A$
$I = 11.32 A$