A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. (i) the terminal velocity achieved by the rod, and the acceleration of the mass at the instant when the velocity of the rod is half the terminal velocity.

A pair of parallel horizontal conducting rails of negligible resistanc

1.	A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. (i) the terminal velocity achieved by the rod, and the acceleration of the mass at the instant when the velocity of the rod is half the terminal velocity.
Answer» Correct Answer - `(i) V_(terminal)=(mgR)/(B^(2)Z^(2)); (ii) g/2` (i) `IlB=mg …(1)n` `I=e/R=(Blv)/R …(2)` From `(1)` and `(2)` `(B^(2)l^(2)v)/R=mg implies v=(mgR)/(B^(2)l^(2))…(3)` (ii) `ma=mg-IlB` `ma=mg-(Bl(v//2)lB)/R=mg-(B^(2)l^(2)v)/(2R)` `=mg-(mg)/2 …(4)` From (3) and (4) `a=g/2`

Discussion

No Comment Found

Related InterviewSolutions

Find the dimension of the quantity L/(RCV), where symbols have usual meaning.
A wire forming one cycle of sine curve is moved in x-y plane with velocity `vec(V)=V_(x)hat(i)+V_(y)hat(j)`. There exist a magnetic field `vec(B)=-B_(0)hat(k)`. Find the motional emf decelop across the ends PQ of wire.
The phase diffenernce between the alternating current and emf is `(pi)/(2)`. Which of the following cannot be the constiuent of the circuit?A. `C` aloneB. `R, L`C. `L, C`D. `L` alone
A horizontal wire is free to slide on the verticle rails of a conducting frame as shown in figure. The wire has a mass `m` and length `l` and the resistance of the circuit is `R`. If a uniform magnetic field `B` is directed perpendicular to the frame, the terminal speed of the wire as it falls under the force of gravity is
An `L-C-R` series circuit with `100Omega` resistance is connected to an `AC` source of `200V` and angular frequency `300rad//s`. When only the capacitance is removed, the current lags behind the voltage by `60^@`. When only the inductance is removed the current leads the voltage by `60^@`. Calculate the current and the power dissipated in the `L-C-R` circuit
A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. (i) the terminal velocity achieved by the rod, and the acceleration of the mass at the instant when the velocity of the rod is half the terminal velocity.
A uniform magnetic field of `0.08 T` is directed into the plane of the page and perpendicular to it as shown in the figure. A wire loop in the plane of the page has constant area `0.010 m^(2)`. The magnitude of magnetic field decrease at a constant rate of `3.0xx10^(-4)Ts^(-1)`. Find the magnitude and direction of the induced enf in the loop.
In series `LR` circuit, `X_(L) = 3 R`. Now a capacitor with `X_(C ) = R` is added in series. The ratio of new to old power factorA. `1`B. `2`C. `1/sqrt(2)`D. `sqrt(2)`
A vertical bar magnet is dropped from from position on the axis of a fixed metallic coil as shown in fig-I. In fig - II the magnet is fixed and horizontal coil is dropped. The accelaration of the magnet and coil are `a_(1)` and `a_(2)` respectively then A. `a_(1)gt g, a_(2) gt g`B. `a_(1)gt g, a_(2) lt g`C. `a_(1)lt g, a_(2) lt g`D. `a_(1)lt g, a_(2) gt g`
Statement 1: In the purely resistive element of a series LCR, ac circuit the maximum value of rms current increase with increase in the angular frequency of the applied emf. Statement 2: `I_(max)=(epsilon_(max))/(Z), Z=sqrt(R^(2)+(omega L-(1)/(omega C)^(2)))`, where `(I_(max))` is the peak current in a cycle.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment