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JEE Physics Solved Question Paper 2009

Multiple Choice Questions

41.
Two copper wires have their masses in the ratio 2 : 3 and the lengths in the ratio 3 : 4.The ratio of their resistances is

4 : 9

27 : 32

16 : 9

27 : 128

27 : 32

The resistance of one wire

$R_{1} = ρ \frac{l_{1}}{A_{1}}$

and the resistance of second wire

$R_{2} = ρ \frac{l_{2}}{A_{2}}$

Ratio of their resistances

$\frac{R_{1}}{R_{2}} = \frac{l_{1}}{A_{1}} \times \frac{A_{2}}{l_{2}}$

Since, mass = density × volume

∴ mass = density × area × length

$or \frac{R_{1}}{R_{2}} = {(\frac{l_{1}}{l_{2}})}^{2} \times \frac{{ρA}_{2} l_{2}}{{ρA}_{1} \times l_{1}} or \frac{R_{1}}{R_{2}} = {(\frac{l_{1}}{l_{2}})}^{2} \times \frac{m_{2}}{m_{1}} or \frac{R_{1}}{R_{2}} = \frac{9}{16} \times \frac{3}{2} or \frac{R_{1}}{R_{2}} = \frac{27}{32}$

R₁ : R₂ = 27 : 32

42.

Two different conductors have same resistance at 0°C. It is found that the resistance of the first conductor at t₁°C is equal to the resistance of the second conductor at t₂°C. The ratio of the temperature coefficients of resistance of the conductors, $\frac{α_{1}}{α_{2}}$ is

$\frac{t_{1}}{t_{2}}$
$\frac{t_{2} - t_{1}}{t_{2}}$
$\frac{t_{2} - t_{1}}{t_{1}}$
$\frac{t_{2}}{t_{1}}$

43.

In the given circuit diagram the current through the battery and the charge on the capacitor respectively in steady state are

1 A and 3 µC
17 A and 0 µC
11 A and 3 µC
6 A and 0 µC

44.

A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 15 V battery and an external resistance 40 Ω. A secondary cell of emf E in the secondary circuit is balanced by 240 cm long potentiometer wire. The emf E of the cell is

2.4 V
1.2 V
2.0 V
3 V

45.

A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram

The resultant magnetic field at the centre of the coil is

zero
$\frac{μ_{0} I}{2 R}$
$\frac{3}{4} (\frac{μ_{0} I}{2 R})$
$\frac{1}{4} (\frac{μ_{0} I}{2 R})$

46.

The resistance of a galvanometer is 50 Ω and it shows full scale deflection for a current of 1 mA. To convert it into a voltmeter to measure 1 V and as well as 10 V (Refer circuit diagram) the resistances R₁ and R₂ respectively are

950 Ω and 9150 Ω
900 Ω and 9950 Ω
900 Ω and 9900 Ω
950 Ω and 9000 Ω

47.

Two long parallel wires carry currents i₁ and i₂ such that i₁ >i₂. When the currents are in the same direction, the magnetic field at a point midway between the wires is 6 x 10^-6 T. If the direction of i₂ is reversed, the field becomes 3 x 10^-5 T. The ratio $\frac{i_{1}}{i_{2}}$ is

$\frac{1}{2}$
2
$\frac{2}{3}$
$\frac{3}{2}$

48.

A coil of 100 turns and area 2 x 10^-2 m², pivoted about a vertical diameter in a uniform magnetic field carries a current of 5A. When the coil is held with its plane in North-South direction, it experiences a torque of 0. 3 Nm. When the plane is in East-West direction the torque is 0.4 Nm. The value of magnetic induction is (Neglect earth's magnetic field)

0.2 T
0.3 T
0.05 T
0.1 T

49.

The angle of dip at a place is 37° and the vertical component of the earth's magnetic field is 6 x 10^-5 T. The earth's magnetic field at this place is (tan 37° = 3/ 4)