Physics Test

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Physics Test - 27

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Weekly Quiz Competition

Question 1
4 / -1

Two different metal rods of the same length have their ends kept at the temperatures \(\theta_{1}\) and \(\theta_{2},\) with \(\theta_{2}>\theta_{1}\)

If \(\mathrm{A}_{1}\) and \(\mathrm{A}_{2}\) are their cross-sectional areas and \(\mathrm{k}_{1}\) and \(\mathrm{k}_{2}\) are their thermal conductivities, then the rate of

flow of heat in the two rods will be the same if

A
\(\frac{A_{1}}{A_{2}}=\frac{k_{1}}{k_{2}}\)

B
\(\frac{A_{1}}{A_{2}}=\frac{k_{2}}{k_{1}}\)

C
\(\frac{A_{1}}{A_{2}}=\frac{k_{1} \theta_{1}}{k_{2} \theta_{2}}\)

D
\(\frac{A_{1}}{A_{2}}=\frac{k_{2} \theta_{2}}{k_{1} \theta_{1}}\)

Solution

Rate of flow is \(\frac{Q}{t}=\frac{k A\left(\theta_{2}-\theta_{1}\right)}{l}\)
since \(\left(\theta_{2}-\theta_{1}\right)\) and \(l\) are the same for the two rods, the rate of flow \(Q / t\) will be the same if the product \(k A\) is the same for the two rods, i.e. if
\[
k_{1} A_{1}=k_{2} A_{2}
\]
or \(\quad \frac{A_{1}}{A_{2}}=\frac{k_{2}}{k_{1}}\)
Hence the correct choice is ( 2 ).
Question 2
4 / -1

If the position of the resultant of two like parallel forces P and Q is unaltered, when the positions of P and Q are interchanged, then

A
P = Q

B
P = 2 Q

C
2 P = Q

D
None of these

Solution

We have \(A C=\left(\frac{A B}{P+Q}\right) Q\) and \(A D=\left(\frac{A B}{P+Q}\right) P\)
since the position of the resultant does not alter
\(\Rightarrow A C=A D \Rightarrow P=Q\)
Question 3
4 / -1

Two batteries \(8 \mathrm{V}\) and \(4 \mathrm{V}\) with respective internal resistances \(4 \Omega\) and \(8 \Omega\) are connected in parallel as shown in the circuit. When switch S is closed, then

A
both the batteries are getting charged.

B
8 V battery is discharging and 4 V battery is charging

C
both batteries are getting discharged

D
4 V battery is discharging and 8 V battery is charging

Solution

\(\mathrm{V}_{\mathrm{AB}}=\mathrm{V}_{\mathrm{CD}}=\mathrm{V}_{\mathrm{EF}}\)
\(\mathrm{V}_{\mathrm{AB}}=8=4 \mathrm{i}_{2}\)
\(\mathrm{V}_{\mathrm{AB}}=4 \mathrm{i}_{2}+8\)
\(V_{C D}=8 i_{2}-4\)
\(\mathrm{V}_{\mathrm{EF}}=4 \mathrm{i}_{1}-\mathrm{i}_{2} 4\)
\(=4 i_{1}+8=-4 i_{1}-i_{2} 4\)
\(8 i_{2}-4 i_{2}=-8\)
\(2 i_{2}++i_{1}=-2 \ldots \ldots \ldots \ldots . .(1)\)
\(8 i_{1}-4=4 i_{1}=4 i_{2}\)
\(12 i_{1}+4 i_{2}=4\)
Or \(\quad 3 i_{1}++i_{2}=1 \ldots \ldots \ldots \ldots .(2)\)
\(i_{1}+2 i_{1}=-2\)
And \(\quad 3 i_{1}+i_{2}=1\)
Solving above two we get
\(i_{1}=0.8\)
\[
\mathrm{i}_{2}=1.4 \mathrm{A}
\]
So from both the batteries current is coming out, so both batteries are discharging
Question 4
4 / -1

A particle acted on by constant forces \(4 \mathrm{i}+\mathrm{j}-3 \mathrm{k}\) and \(3 \mathrm{i}+\mathrm{j}-\mathrm{k}\) to the point \(5 \mathrm{i}+4 \mathrm{j}+\mathrm{k} \cdot\) The total work done by the forces is

A
20 units

B
30 units

C
40 units

D
50 units

Solution

\(\vec{F}+\vec{F}_{1}+\vec{F}_{2}=7 i+2 j-4 k\)
\(\vec{d}=P \cdot V \cdot\) of \(\vec{B}-P \cdot V \cdot\) of \(\vec{A}=4 i+2 j-2 k\)
\(W=\vec{F} \cdot \vec{d}=28+4+8=40 \mathrm{unit}\)
Question 5
4 / -1

The condition for a uniform spherical mass 'm' of radius 'r', to be a black hole is ______________.

[G = gravitational constant and g = acceleration due to gravity]

A
\(\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c\)

B
\(\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c\)

C
\(\left(\frac{2 G m}{r}\right)^{1 / 2} \geq c\)

D
\(\left(\frac{G m}{r}\right)^{1 / 2} \geq c\)

Solution

\(\left(\frac{2 G m}{r}\right)^{1 / 2} \geq c\)

Is the necessary condition for a spherical mass m of radius r to be a black hole.
Question 6
4 / -1

A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly

A
14 rpm

B
10 rpm

C
2.25 rpm

D
7 rpm

Solution

As \(T=m \omega^{2} r\)
for \(T^{\prime}=2 T,\) let \(\omega^{\prime}\) is final angular velocity
\(T^{\prime}=m \omega^{\prime 2} r\)
\(\frac{T^{\prime}}{T}=\frac{\omega^{\prime 2}}{\omega^{2}}=2\)
\(\omega^{\prime}=\sqrt{2} \omega\) greater is the angular velocity greater are the number of revolutions
So angular speed will be 7 revolutions per min
Question 7
4 / -1

An AND gate has four inputs A, B, C, D. The input that produces an output 1 is

A
0000

B
1000

C
0001

D
1111

Solution

An AND gate always produces an output 1, only when all the inputs are 1.
Question 8
4 / -1

In a transistor circuit, the collector current is 50 mA and the base current is 1 mA. The current gain α is

A
51/50

B
49/50

C
50/51

D
49/51

Solution

Current gain, \(\beta=\frac{\mathrm{lc}}{\mathrm{l}_{\mathrm{B}}}=\frac{50}{1}=50\)
Therefore, current gain, \(\alpha=\frac{\beta}{1+\beta}=\frac{50}{1+50}=\frac{50}{51}\)
Hence, the correct choice is (3).
Question 9
4 / -1

Weight of a body of mass decreases by 1% when it is raised to height 'h' above Earth's surface. If the body is taken to a depth 'h' in a mine, the change in its weight is

A
2% decrease

B
1% decrease

C
0.5% decrease

D
0.5% increase

Solution

At height \(h, \frac{g^{\prime}-g}{g}=-\frac{2 h}{R_{t}}=-1 \%\)
At depth \(d, \frac{g^{n}-g}{g}=-\frac{h}{R_{e}}=-\frac{1}{2} \Re=-0.5 \%\)
Weight is mine will decrease by \(0.5 \%\)
Question 10
4 / -1

What is the dimension of \(\frac{L}{R C V},\) where \(L, R, C\) and \(V\) have their usual meanings?

A
M¹L¹A^-2T⁰

B
M⁰L^-1A^-1F¹

C
M¹L⁰A ^-1 T⁰

D
M⁰L⁰A^-1T⁰

Solution

\(\mathrm{emf}=\mathrm{V}=\mathrm{L} \mathrm{d} 1 / \mathrm{dt}\)
\(\mathrm{L}=\mathrm{V} \mathrm{dt} / \mathrm{d} \mid\)
\(\mathrm{RC}\) is time constant. Its dimension is equal to time. So, dimension of \(\frac{L}{R C V}=V d t / d l\) \(\mathrm{RCV}=1 / \mathrm{A}=\mathrm{M}^{0} \mathrm{L}^{0} \mathrm{A}^{-1} \mathrm{T}^{0}\)

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Physics Test - 27

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Physics Test - 27

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Question 1

\(\frac{A_{1}}{A_{2}}=\frac{k_{1}}{k_{2}}\)

\(\frac{A_{1}}{A_{2}}=\frac{k_{2}}{k_{1}}\)

\(\frac{A_{1}}{A_{2}}=\frac{k_{1} \theta_{1}}{k_{2} \theta_{2}}\)

\(\frac{A_{1}}{A_{2}}=\frac{k_{2} \theta_{2}}{k_{1} \theta_{1}}\)

Solution

Question 2

P = Q

P = 2 Q

2 P = Q

None of these

Solution

Question 3

both the batteries are getting charged.

8 V battery is discharging and 4 V battery is charging

both batteries are getting discharged

4 V battery is discharging and 8 V battery is charging

Solution

Question 4

20 units

30 units

40 units

50 units

Solution

Question 5

\(\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c\)

\(\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c\)

\(\left(\frac{2 G m}{r}\right)^{1 / 2} \geq c\)

\(\left(\frac{G m}{r}\right)^{1 / 2} \geq c\)

Solution

Question 6

14 rpm

10 rpm

2.25 rpm

7 rpm

Solution

Question 7

0000

1000

0001

1111

Solution

Question 8

51/50

49/50

50/51

49/51

Solution

Question 9

2% decrease

1% decrease

0.5% decrease

0.5% increase

Solution

Question 10

M1L1A-2T0

M0L-1A -1F1

M1L0A -1 T0

M0L 0A-1T0

Solution

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M¹L¹A^-2T⁰

M⁰L^-1A^-1F¹

M¹L⁰A ^-1 T⁰

M⁰L⁰A^-1T⁰