Physics Test

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Physics Test - 22

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Question 1
1 / -0

The charge on a particle Y is double the charge on particle X. These 2 particles X and Y after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii r₁ and r₂ respectively. Find ratio of the mass of X to that of Y.

A

\(\frac{2 R_{1}}{R_{2}}\)

B

\(\frac{R_{1}^{2}}{2 R_{2}^{2}}\)

C

\(\left(\frac{R_{1}}{2 R_{2}}\right)^{2}\)

D

\(\left(\frac{2 \mathrm{R}_{2}}{\mathrm{R}_{2}}\right)^{2}\)

Solution

Here, \(r=\frac{1}{B} \sqrt{\frac{2 m V}{q}} \Rightarrow r \propto \sqrt{\frac{m}{q}}\)
\(\Rightarrow \frac{r_{x}}{r_{y}} \times \sqrt{\frac{m_{x}}{q_{x}} \times \frac{q_{y}}{m_{y}}}\)
\(\Rightarrow \frac{R_{1}}{R_{2}}=\sqrt{\frac{m_{x}}{m_{y}} \times \frac{2}{1}} \Rightarrow \frac{m_{x}}{m_{y}}=\frac{R_{1}^{2}}{2 R_{2}^{2}}\)
Question 2
1 / -0

An electron of mass 'm' and charge 'q' is travelling with a speed 'v' along a circular path of radius 'r' at right angles to a uniform of magnetic field B. If speed of the electron is doubled and the magnetic field is halved, then what would be the resulting path?

A
4r

B
2r

C
r/4

D
r/2

Solution

We know,

\(r=\frac{m v}{g B}\)
\(\Rightarrow \frac{r_{1}}{r_{2}}=\frac{v_{1}}{v_{2}} \times \frac{b_{2}}{B_{1}} \Rightarrow \frac{r_{1}}{r_{2}}=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\)
\(\Rightarrow r_{2}=4 r_{1}\)
Question 3
1 / -0

A proton of energy 8 eV is moving in a circular path in a uniform magnetic field. What will be energy of an alpha particle moving in the same magnetic field and along the same path?

A
2 eV

B
4 eV

C
6 eV

D
8 eV

Solution

We know, \(r=\frac{\sqrt{2 m k}}{q B} \Rightarrow q \alpha \sqrt{m k} \Rightarrow k \propto \frac{q^{2}}{m}\)
\(\Rightarrow \frac{k_{a}}{K_{p}}=\left(\frac{q_{a}}{q_{p}}\right)^{2} \times \frac{m_{p}}{m_{a}}\)
\(\Rightarrow \frac{K_{a}}{8}=\left(\frac{2 q_{p}}{q_{p}}\right)^{2} \times \frac{m_{p}}{4 m_{p}}=1\)
\(\rightarrow K_{a}=8 e V\)
Question 4
1 / -0

A copper wire of length 1 m and radius 1 mm is connected in series with an iron wire of length 2 m and radius 3 mm and a current is passed through the wires. Find the ratio of the current density in the copper and iron wires.

A
2:3

B
6:1

C
9:1

D
18:1

Solution

Current density, \(J=\frac{i}{A}=\frac{i}{\pi r^{2}}\)
\(\Rightarrow \frac{\mathrm{J}_{1}}{\mathrm{J}_{2}}=\frac{\mathrm{i}_{1}}{\mathrm{i}_{2}} \times \frac{\mathrm{r}_{2}^{2}}{\mathrm{r}_{1}^{2}}\)
But the wires are in series, thus they have the same current, hence \(i_{1}=i_{2}\)
\(\rightarrow \frac{\mathrm{J}_{1}}{\mathrm{J}_{2}}=\frac{\mathrm{r}_{2}^{2}}{\mathrm{r}_{1}^{2}}=9: 1\)
Question 5
1 / -0

How much amount of charge is flowing in 2 minutes in a wire of resistance 10 when a potential difference of 20 V is applied between its ends?

A
240 C

B
120 C

C
20 C

D
4 C

Solution

\(A s, i=\frac{V}{B}=\frac{Q}{E}\)
\(\Rightarrow Q=\frac{V t}{R}=\frac{\sum_{0} \times 2 \times 60}{10}=240 \mathrm{c}\)
Question 6
1 / -0

The length of a given cylindrical wire is raised by 100%. What will be the change in the resistance of the wire due to the consequent decrease in diameter?

A
50%

B
100%

C
200%

D
300%

Solution

Consider initial length \(l_{1}=100,\) then \(I_{2}=100+100=200\)
\[
\begin{array}{l}
\text { and } \frac{R_{1}}{R_{2}}=\left(\frac{l_{1}}{I_{2}}\right)^{2}=\left(\frac{100}{200}\right)^{2} \Rightarrow R_{2}=4 R_{1} \\
\Rightarrow \frac{\Delta R}{R} \times 100=\frac{R_{2}-R_{1}}{R_{1}} \times 100=\frac{4 R_{1}-R_{1}}{R_{1}} \times 100 \\
\Rightarrow \frac{\Delta R}{R}=300 \%
\end{array}
\]
Question 7
1 / -0

A magnet vibrates in a horizontal plane at 2 places A and B using vibration magnetometer. Its respective periodic times are 2 s and 3 s and at these places the earth's horizontal components are H_A and H_B respectively. Then what will be the ratio between H_A and H_B?

A
2:3

B
3:2

C
4:9

D
9:4

Solution

Time period, \(\mathrm{T}=2 \pi \sqrt{\frac{1}{\mathrm{MH}}}\) i.e. \(\mathrm{T} \propto \frac{1}{\sqrt{\mathrm{H}}}\)
\(\Rightarrow \frac{T_{A}}{T_{B}}=\sqrt{\frac{H_{B}}{H_{A}}}\)
\(\Rightarrow \frac{\mathrm{H}_{\mathrm{A}}}{\mathrm{H}_{\mathrm{B}}}=\left(\frac{\mathrm{T}_{\mathrm{B}}}{\mathrm{T}_{\mathrm{A}}}\right)^{2}=\left(\frac{3}{2}\right)^{2}=\frac{9}{4}\)
Question 8
1 / -0

Two charges of 4 mu C each are situated at the corners A and B of an equilateral triangle of side length 0.2 m in air. What is the electric potential at C?

\(\mathrm{}\left[\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \frac{\mathrm{N}-\mathrm{m}^{2}}{\mathrm{C}^{2}}\right]\)

A
36 x 10^-4 V

B
36 x 10⁴ V

C
18 x 10⁴ V

D
9 x 10⁴ V

Solution
Question 9
1 / -0

2 ions having masses in the ratio 1:1 and charges 1:2 are projected into uniform magnetic field perpendicular to the field with speeds in the ratio 2:3. What is the ratio of the radii of circular paths along which the 2 particles move?

A
1:4

B
3:1

C
2:3

D
4:3

Solution

\(A S, r=\frac{m v}{q B} \Rightarrow \frac{r_{1}}{r_{2}}=\frac{m_{1} v_{1}}{m_{2} v_{2}} \times \frac{q_{2}}{q_{2}}\)
\(\Rightarrow \frac{r_{1}}{r_{2}}=\frac{1 \times 2}{1 \times 3} \times \frac{2}{1}=\frac{4}{3}\)
Question 10
1 / -0

2 magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together, 12 oscillations per minute are made but for unlike poles together only 4 oscillations per minute are executed. What will be ratio of their magnetic moments?

A
5:4

B
3:5

C
1:3

D
3:1

Solution

In the sum and difference method of vibration magnetometer, we have

\(\frac{M_{1}}{M_{2}}=\frac{T_{2}^{2}+T_{1}^{2}}{T_{2}^{2}-T_{1}^{2}}\)
Here, \(T_{1}=\frac{1}{n_{1}}=\frac{60}{12}=5 \mathrm{s}\) and \(T_{2}=\frac{1}{n_{2}}=\frac{60}{4}=15 \mathrm{s}\)
\(\therefore \frac{M_{1}}{M_{2}}=\frac{15^{2}+5^{2}}{15^{2}-5^{2}}=\frac{225+25}{225-25}=\frac{5}{4}\)

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Re-Attempt Weekly Quiz Competition

Physics Test - 22

Result

Physics Test - 22

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SHARING IS CARING

Question 1

\(\frac{2 R_{1}}{R_{2}}\)

\(\frac{R_{1}^{2}}{2 R_{2}^{2}}\)

\(\left(\frac{R_{1}}{2 R_{2}}\right)^{2}\)

\(\left(\frac{2 \mathrm{R}_{2}}{\mathrm{R}_{2}}\right)^{2}\)

Solution

Question 2

4r

2r

r/4

r/2

Solution

Question 3

2 eV

4 eV

6 eV

8 eV

Solution

Question 4

2:3

6:1

9:1

18:1

Solution

Question 5

240 C

120 C

20 C

4 C

Solution

Question 6

50%

100%

200%

300%

Solution

Question 7

2:3

3:2

4:9

9:4

Solution

Question 8

36 x 10-4 V

36 x 104 V

18 x 104 V

9 x 104 V

Solution

Question 9

1:4

3:1

2:3

4:3

Solution

Question 10

5:4

3:5

1:3

3:1

Solution

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36 x 10^-4 V

36 x 10⁴ V

18 x 10⁴ V

9 x 10⁴ V