please show me the calculations for getting to the answers. The answers are A, D

Question

please show me the calculations for getting to the answers.

The answers are A, D, and C, respectively.

A conducting rectangular loop of mass M, resistance R, and dimensions nxb is allowed to fall from rest through a uniform magnetic field which is perpendicular to the plane of the loop. The loop accelerates until it reaches a terminal speed (before the upper end enters the magnetic field). If u = 2.0m, B = 6.0 T, R = 40 n, and M = 0.60 kg, what is the terminal speed? 1.6 m/s 20 m/s 2.2 m/s 26 m/s 5.3 m/s A conducting rod (length = SO cm) rotates at a constant angular rate of 15 revolutions per second about a pivot at one end. A uniform field (B = 60 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the emf induced between the ends of the rod? 2.7 V 2.1V 2.4 V 1.8 V 3.3 V A metal blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade. This rotation occurs in a region where the component of the earth's magnetic field perpendicular to the blade is 30 mu T. If the blade is 60 cm in length, what is the magnitude of the potential difference between its ends? 0.24 mV 0.20 mV 0.17 mV 0.27 mV 0.34 mV

Explanation / Answer

Mg=ILB

induced emf=e=BVL

v=rw

e=IR

Mg=(e/R)*L*B

( BVL/R)*L*B

=B^2L^2V/R

v=RMg/(B^2L^2)

=40*0.6*9.81/(6^2)*(2^2)

=1.6m/s

B) for coil

E=induced emf = 2*pi*N*(B*L^2*w/2)

here N=1 w=15 L=80cm B=60mT

by calculationg

(2*3.14*1*60*10^-3*(80*10^-2)^2*15)/2 = 1.8v

C)

same formula for coil

   E=induced emf = 2*pi*N*(B*L^2*w/2)

here N=1

w=5

L=60cm

B=30uT

by calculationg

(2*3.14*1*30*10^-6*(60*10^-2)^2*5)/2 = 0.17mV

sorry the photo that i posted was not uploded

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